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Journal of the American Mathematical Society This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

Subscription information. The Journal of the American Mathematical Society is published quarterly. Subscription prices for Volume 5 (1992) are $136 list, $109 institutional member, $82 individual member. Subscribers outside the United States and India must pay a postage surcharge of $8; subscribers in India must pay a postage surcharge of $18. Expedited delivery to destinations in North America $13; elsewhere $36. Back number information. For back issues see the AMS Catalogue of Publications. Subscriptions and orders should be addressed to the American Mathematical Soci- ety, P.O. Box 1571, Annex Station, Providence, RI02901-1571. All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, RI 02940-6248. Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews provided the customary acknowledgement of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248. The appearance of the code on the first page of an article in this journal indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, MA 01970. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale.

The Journal ofthe American Mathematical Society is published quarterly by the Amer- ican Mathematical Society at 201 Charles Street, Providence, RI 02904-2213 and is mailed from Providence, Rhode Island. Second class postage is pending at Providence, Rhode Island. Postmaster: Send address changes to Journal of the AMS, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248.

Copyright © 1992 by the American Mathematical Society. All rights reserved. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. § This publication was typeset using AA1S-TEX, the American Mathematical Society's TEX macro system. 109876 5432 1 979695949392 INDEX TO VOLUME 5 January-December 1992

Aschbacher, Michael and Segev, Yoav. The uniqueness ofgroups of Lyons type, 75 Attie, Oliver, Block, Jonathan, and Weinberger, Shmuel. Characteristic classes and distortion of dijfeomorphisms, 919 Benoist, Yves. See Foulon, Patrick Bielefeld, Ben, Fisher, Yuval, and Hubbard, John. The classification of critically preperiodic polynomials as dynamical systems, 721 Bjorner, Anders and Ziegler, Giinter M. Combinatorial stratification ofcomplex arrangements, 105 Block, Jonathan and Weinberger, Shmuel. Aperiodic tilings, positive scalar curvature, and amenability of spaces, 907 ---. See Attie, Oliver Caffarelli, Luis A. The regularity of mappings with a convex potential, 99 Cheeger, Jeff, Fukaya, Kenji, and Gromov, Mikhael. Nilpotent structures and invariant metrics on collapsed manifolds, 327 Culler, Marc and Shalen, Peter B. Paradoxical decompositions, 2-generator Kleinian groups, and volumes of hyperbolic 3-manifolds, 231 De Concini, c., Kac, V. G., and Procesi, C. Quantum coadjoint action, 151 Denef, J. and Loeser, F. Caracteristiques d'Euler-Poincare, fonctions zeta locales et modifications analytiques, 705 Fisher, Yuval. See Bielefeld, Ben Foulon, Patrick, Benoist, Yves, and Labourie, Francois. Flots d'Anosov i1 distribution stable et instable dijferentiables, 33 Fukaya, Kenji. See Cheeger, Jeff Ginzburg, Viktor L. and Weinstein, Alan. Lie-Poisson structure on some Poisson Lie groups, 445 Gromov, Mikhael. See Cheeger, Jeff Hubbard, John. See Bielefeld, Ben Kac, V. G. See De Concini, C. Kim, K. H. and Roush, F. W. Williams's conjecture is false for reducible subshi/ts, 213 Kim, K. H., Roush, F. W., and Wagoner, J. B. Automorphisms ofthe dimension group and gyration numbers, 191 Kirwan, Frances. The cohomology rings of moduli spaces of bundles over Riemann surfaces, 853 Kollar, Janos and Mori, Shigefumi. Classification of three-dimensional flips, 533 Kottwitz, Robert E. Points on some Shimura varieties over finite fields, 373 Labourie, Francois. See Foulon, Patrick LeBrun, Claude. Twistors, Kahler manifolds, and bimeromorphic geometry. I, 289 LeBrun, Claude and Poon, Vat-Sun. Twistors, Kahler manifolds, and bimeromorphic geometry. II, 317 Lempert, Laszlo. On three-dimensional Cauchy-Riemann manifolds, 923 Lenstra, H. W., Jr. and Pomerance, Carl. A rigorous time bound for factoring integers, 483 Li, Chun, Mcintosh, Alan, and Semmes, Stephen. Convolution singular integrals on Lipschitz surfaces, 455 Loeser, F. See Denef, J. Lusztig, G. Remarks on computing irreducible characters, 971 McDuff, Dusa. Erratum to "The structure of rational and ruled symplectic 4-manifolds", 987 Mcintosh, Alan. See Li, Chun Mori, Shigefumi. See Kollar, Janos Phillips, R. and Sarnak, P. Perturbation theory for the Laplacian on automorphic functions, I Pomerance, Carl. See Lenstra, H. W., Jr. Poon, Vat-Sun. See LeBrun, Claude Procesi, C. See De Concini, C. INDEX TO VOLUME 5

Radulescu, Florin. The fundamental group of the von Neumann algebra of a free group with infinitely many generators is R+ \ {O}, 517 Roush, F. W. See Kim, K. H. Sarnak, P. See Phillips, R. Segev, Yoav. See Aschbacher, Michael Semmes, Stephen. See Li, Chun Shalen, Peter B. See Culler, Marc Stanley, Richard P. Subdivisions and local h-vectors, 805 Thomassen, Carsten. The even cycle problem for directed graphs, 217 Vojta, Paul. A generalization of theorems of Faltings and Thue-Siegel-Roth-Wirsing, 763 Wagoner, J. B. See Kim, K. H. Weinberger, Shmuel. See Attie, Oliver --. See Block, Jonathan Weinstein, Alan. See Ginzburg, Viktor L. Ziegler, Gunter M. See Bjorner, Anders VOLUME 5 1992

AMERICAN MATHEMATICAL SOCIETY

EDITORS H. Blaine Lawson, Jr. Robert D. MacPherson Richard Melrose Andrew Odlyzko Wilfried Schmid

ASSOCIATE EDITORS James G. Arthur Persi Diaconis Gerd Faltings Charles L. Fefferman Michael H. Freedman Ronald L. Graham Joe Harris Andrew Majda Dusa McDuff Hugh L. Montgomery Marina Ratner Richard Schoen Richard Stanley W. Hugh Woodin

PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 Journal of the American Mathematical Society This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

Back number information. For back issues see the AMS Catalogue of Publications. Subscriptions and orders should be addressed to the American Mathematical Soci- ety, P.O. Box 1571, Annex Station, Providence, RI02901-1571. All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, RI 02940-6248. Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews provided the customary acknowledgement of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248. The appearance of the code on the first page of an article in this journal indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, MA 01970. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale.

Copyright © 1992 by the American Mathematical Society. All rights reserved. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. €9 This publication was typeset using Aj\.1S-TEX, the American Mathematical Society'S TEX macro system. 10 9 8 7 6 5 4 3 2 1 97 96 95 94 93 92 Journal of the American Mathematical Society

Volume S, Number 1 January 1992

Perturbation theory for the Laplacian on automorphic functions R. PHILLIPS AND P. SARNAK ......

Flots d'Anosov a distribution stable et instable differentiables PATRICK FOULON, YVES BENOIST, ET FRANCOIS LABOURIE 33

The uniqueness of groups of Lyons type MICHAEL ASCHBACHER AND YOAV SEGEV...... 75

The regularity of mappings with a convex potential LUIS A. CAFFARELLI ...... 99

Combinatorial stratification of complex arrangements ANDERS BJORNER AND GUNTER M. ZIEGLER...... 105

Quantum coadjoint action C. DE CONCINI, V. G. KAc, AND C. PROCESI ...... 151

Automorphisms of the dimension group and gyration numbers K. H. KIM, F. W. ROUSH, AND J. B. WAGONER...... 191

Williams's conjecture is false for reducible subshifts K. H. KIM AND F. W. ROUSH...... 213

Volume S, Number 2 April 1992

The even cycle problem for directed graphs CARSTEN THOMASSEN...... 217

Paradoxical decompositions, 2-generator Kleinian groups, and volumes of hyperbolic 3-manifolds MARC CULLER and PETER B. SHALEN ...... 231

Twistors, Kahler manifolds, and bimeromorphic geometry. I CLAUDE LEBRUN...... 289 Twistors, Kahler manifolds, and bimeromorphic geometry. II CLAUDE LEBRUN and VAT-SUN POON ...... 317

Nilpotent structures and invariant metrics on collapsed manifolds JEFF CHEEGER, KENJI FUKAYA, and MIKHAEL GROMOV...... 327

Points on some Shimura varieties over finite fields ROBERT E. KOTTWITZ ...... 373

Lie-Poisson structure on some Poisson Lie groups VIKTOR L. GINZBURG and ALAN WEINSTEIN ...... 445

Volume 5, Number 3 July 1992

Convolution singular integrals on Lipschitz surfaces CHUN LI, ALAN McINTOSH, and STEPHEN SEMMES ...... 455

A rigorous time bound for factoring integers H. W. LENSTRA, JR. and CARL POMERANCE...... 483

The fundamental group of the von Neumann algebra of a free group with infinitely many generators is R+ \{O} FLORIN RADULESCU ...... 517

Classification of three-dimensional flips JANOS KOLLAR and SHIGEFUMI MORI ...... 533

Volume 5, Number 4 October 1992

Caracteristiques d'Euler-Poincare, fonctions zeta locales et modifications analytiques J. DENEF ET F. LOESER ...... 705

The classification of critically preperiodic polynomials as dynamical systems BEN BIELEFELD, YUVAL FISHER, and JOHN HUBBARD ...... 721

A generalization of theorems of Faltings and Thue-Siegel-Roth-Wirsing PAUL VOJTA ...... 763 Subdivisions and local h-vectors RICHARD P. STANLEY...... 805

The cohomology rings of moduli spaces of bundles over Riemann surfaces FRANCES KIRWAN...... 853

Aperiodic tilings, positive scalar curvature, and amenability of spaces JONATHAN BLOCK and SHMUEL WEINBERGER ...... 907

Characteristic classes and distortion of diffeomorphisms OLIVER ATTIE, JONATHAN BLOCK, and SHMUEL WEINBERGER..... 919

On three-dimensional Cauchy-Riemann manifolds LASZLO LEMPERT ...... 923

Remarks on computing irreducible characters G. LUSZTIG ...... 971

Erratum to "The structure of rational and ruled symplectic 4-manifolds" DUSA McDuFF...... 987 Editors Chairman Wilfried Schmid Department of Mathematics Harvard University Cambridge, MA 02138 H. Blaine Lawson, Jr. Richard Melrose Department of Mathematics Department of Mathematics 2-243 SUNY at Stony Brook Massachusetts Institute of Technology Stony Brook, NY 11794 Cambridge, MA 02139 Robert D. MacPherson Andrew Odlyzko Department of Mathematics 2-246 Room 2C-355 Massachusetts Institute of Technology AT & T Bell Laboratories Cambridge, MA 02139 600 Mountain Avenue Murray Hill, NJ 07974

Associate Editors James G. Arthur, University of Toronto Persi Diaconis, Harvard University Gerd Faltings, Princeton University Charles L. Fefferman, Princeton University Michael H. Freedman, University of California, San Diego Ronald L. Graham, AT & T Bell Laboratories Joe Harris, Harvard University Andrew Majda, Princeton University Dusa McDuff, SUNY at Stony Brook Hugh L. Montgomery, University of Michigan Marina Ratner, University of California, Berkeley Richard Schoen, Stanford University Richard Stanley, Massachusetts Institute of Technology W. Hugh Woodin, University of California, Berkeley Assistant to the Editorial Board Joanne Jonsson Department of Mathematics 2-108 Massachusetts Institute of Technology Cambridge, MA 02139

Editorial Information As of August 1, 1992, the backlog for this journal was approximately 2 issues. This estimate is the result of dividing the number of manuscripts for this journal in the Providence office that have not yet gone to the printer on the above date by the average number of articles per issue over the previous twelve months. A Copyright Transfer Agreement is required before a paper will be published in this journal. By submitting a paper to this journal, authors certify that the manuscript has not been submitted to nor is it under consideration for publication by another journal, conference proceedings, or similar pUblication. Information for Authors The first page must contain a descriptive title that is short, but informative; useless or vague phrases such as "some remarks about" or "concerning" should be avoided. Included with the footnotes to the paper, there should be the 1991 Mathematics Subject Classification representing the primary and secondary sub- jects of the article. This may be followed by a list of key words and phrases de- scribing the subject matter of the article and taken from it. A list of the numbers may be found in the annual index of Mathematical Reviews, published with the December issue starting in 1990, as well as from the electronic service e-MATH [teinet e-MATH.ams.com (or teinet 130.44.1.100). Login and password are e- math]. For journal abbreviations used in bibliographies, see the list of serials in the latest Mathematical Reviews annual index. When the manuscript is submitted, authors should supply the editor with electronic addresses if available. These will be printed after the postal address at the end of each article. Electronically-prepared manuscripts. The AMS encourages submission of electronically-prepared manuscripts in A.A;tS-TEX or AMS-Jb.TEX because prop- erly prepared electronic manuscripts save the author proofreading time and move more quickly through the production process. To this end, the Society has prepared "preprint" style files, specifically the amsppt style of A.A;tS-TEX and the amsart style of .A"w5-Jb.TEX, which will simplify the work of authors and of the production staff. Those authors who make use of these style files from the beginning of the writing process will further reduce their own effort. Guidelines for Preparing Electronic Manuscripts provide additional assistance and are available for use with either A.A;tS-TEX or AMS-Jb.TEX. Authors with FTP access may obtain these Guidelines from the Society's Internet node e-MATH.ams.com (130.44.1.100). For those without FTP access they can be obtained free of charge from the e-mail [email protected] (In- ternet) or from the Publications Department, P. O. Box 6248, Providence, RI 02940-6248. When requesting Guidelines please specify which version you want. Electronic manuscripts should be sent to the Providence office only after the paper has been accepted for publication. Please send electronically prepared manuscript files via e-mail [email protected] (Internet) or on diskettes to the Publications Department address listed above. When submitting electronic manuscripts please be sure to include a message indicating in which publication the paper has been accepted. Two copies of the paper should be sent directly to one of the Editors or to the Assistant to the Editorial Board and the author should keep one copy. At that time authors should indicate if the paper has been prepared using A.A;tS-TEX or AMS-Jb.TEX. The Manual for Authors of Mathematical Papers should be con- sulted for symbols and style conventions. The Manual may be obtained free of charge from the e-mail address [email protected] or from AMS, Cus- tomer Services Department, P. O. Box 6248, Providence, RI 02940-6248. Any inquiries concerning a paper that has been accepted for publication should be sent directly to the Editorial Department, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248.