VOLUME 3 NUMBER 4 OCTOBER 1990

AMERICANMATHEMATICALSOCIETY

EDITORS Michael Artin H. Blaine Lawson, Jr. Richard Melrose Wilfried Schmid Robert E. Tarjan ASSOCIATE EDITORS James G. Arthur Peter Bickel Gerd Faltings Charles L. Fefferman Michael H. Freedman Daniel Friedan Ronald L. Graham Joe Harris Hendrik W. Lenstra, Jr. Andrew Majda Hugh L. Montgomery Paul H. Rabinowitz Karen Uhlenbeck W. Hugh Woodin

PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 Joumal of the American Mathematical Society The Journal of the American Mathematical Society has been established for the publication of research articles in all areas of pure and applied mathematics. EDITORS Chairman Michael Artin Department of Mathematics 2-239 Massachusetts Institute of Technology Cambridge, MA 02139 H. Blaine Lawson, Jr. Wilfried Schmid Department of Mathematics Department of Mathematics SUNY at Stony Brook Harvard University Stony Brook, NY 11794 Science Center 430 Cambridge, MA 02138 Richard Melrose Robert E. Tarjan Department of Mathematics 2-ISO Department of Computer Science Massachusetts Institute of Technology Princeton University Cambridge, MA 02139 Princeton, NJ 08544

ASSOCIATE EDITORS James G. Arthur, University of Toronto Peter Bickel, University of California, Berkeley Gerd Faltings, Princeton University Charles L. Fefferman, Princeton University Michael H. Freedman, University of California, San Diego Daniel Friedan, University of Chicago Ronald L. Graham, AT & T Bell Laboratories Joe Harris, Harvard University Hendrik W. Lenstra, Jr., University of California, Berkeley Andrew Majda, Princeton University Hugh L. Montgomery, University of Michigan Paul H. Rabinowitz, University of Wisconsin Karen Uhlenbeck, University of Texas at Austin W. Hugh Woodin, University of California, Berkeley Subscription information. The Journal of the American Mathematical Society is published quar- terly. Subscription prices for Volume 3 (1990) are $116 list, $93 institutional member, $70 indi- vidual member. Subscribers outside the United States and India must pay a postage surcharge of $S; subscribers in India must pay a postage surcharge of $IS. Back number information. Back number prices per volume are: for Volume I, $1 SS list, $124 institutional member; for Volume 2, $167 list, $134 institutional member. Manuscript submission. See inside back cover.

Subscriptions and orders for publications of the American Mathematical Society should be addressed to American Mathematical Society, P.O. Box 1571, Annex Station, Providence, R.I. 02901-1571. All orders must be accompanied by payment. Other correspondence should be addressed to P.O. Box 6248, Providence, R.I. 02940-6248. The Journal of the American Mathematical Society is published Quarterly by the American Mathematical Society at 201 Charles Street, Providence, R.I. 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. R.I. 02940-6248. Copyright © 1990 American Mathematical Society. All rights reserved. Printed in the United States of America Information on Copying and Reprinting can be found at the back of this journal. The paper used in this journal is acid-free and falls within the~uidelines established to ensure permanence and durability. ~ This publication was typeset using AMoS-TEX. the American Mathematical Society's TEX macro system. 1098765432 01 00 99 98 97 INDEX TO VOLUME 3 January-December 1990

Abresch, Uwe and Gromoll, Detlef. On complete manifolds with nonnegative Ricci curvature, 355 Alon, Noga, Seymour, Paul, and Thomas, Robin. A separator theorem for nonplanar graphs, 801 Andrews, George E. Euler's "'Exemplum memorabile inductionis fallacis" and q-trinomial coefficients, 653 Bass, Hyman and Kulkarni, Ravi. Uniform tree lattices, 843 Bismut, Jean-Michel. Koszul complexes, harmonic oscillators, and the Todd class, 159 Burns, Daniel M. and Epstein, Charles L. Embeddabi/ity for three-dimensional CR-manifolds, 809 Chang, Sun-Yung A. and Yang, Paul C. P. Isospectral conformal metrics on 3-manifolds, 117 Diaconis, Persi and Rockmore, Daniel. Efficient computation of the Fourier transform on finite groups, 297 Donnelly, Harold and Fefferman, Charles. Nodal sets for eigenfunctions of the Laplacian on sur- faces, 333 Epstein, Charles L. See Burns, Daniel M. Fefferman, Charles. See Donnelly, Harold Frankl, P. and ROdI, V. A partition property of simplices in Euclidean space, I Friedman, Sy. D. The n~-Singleton Conjecture, 771 Goodman, Richard. See Pollack, Jacob E. Gromoll, Detlef. See Abresch, Uwe Gross. Benedict H. Group representations and lattices, 929 Grove, Karsten and Petersen, Peter V. A pinching theorem for homotopy spheres, 671 Guillemin, V. Inverse spectral results on two-dimensional tori, 375 Habegger,Nathan and Lin, Xiao-Song. The classification of links up to lirlk-homotopy, 389 Harrington, L. A., Kechris, A. S., and Louveau, A. A Glimm-Effros dichotomy for Borel equivalence relations, 903 Hochster, Melvin and Huneke, Craig. Tight closure, invariant theory, and the Brian~on-Skoda Theorem, 31 Huneke, Craig. See Hochster, Melvin Kechris, A. S. See Harrington, L. A. Kra, Irwin. Horocyclic coordinates for Riemann surfaces and moduli spaces. 1: Teichmiiller and Riemann spaces of Kleinian groups, 499 Kulkarni, Ravi. See Bass, Hyman Louveau, A. See Harrington, L. A. Lubotzky, Alexander. Lattices ofminimal covolume in SL2: a nonarchimedean analogue ofSiegel's theorem J.l ~ n/21, 961 Lusztig, G. Canonical bases arising from quantized enveloping algebras, 447 Lusztig, George. Finite dimensional Hopf algebras arising from quantized universal enveloping al- gebras, 257 McCanhy, John E. Common range ofco-analytic Toeplitz operators, 793 McDuff, Dusa. The structure of rational and ruled symplectic 4-manifolds, 679 Petersen, Peter V. See Grove, Karsten Pollack, Jacob E., Goodman, Richard, and Sturmfels, Bernard. The intrinsic spread of a configu- ration in Rd, 639 Pollen, David. SUr(2, F[z, liz]) for Fa subfield ofC, 611 ROdI, V. See Frankl, P. Rockmore, Daniel. See Diaconis, Persi Seymour, Paul. See Alon, Noga Shing, Tung Yau. See Tian, G. Simpson, Carlos T. Harmonic bundles on noncompact curves, 713 INDEX TO VOLUME 3

Soergel, Wolfgang. Kategorie~, perverse Garben und Moduln uber den Koinvarianten zur Weylgruppe, 421 Sturmfels, Bernard. See Pollack, Jacob E. Talagrand, Michel. The three-space problem for L 1, 9 Thomas, Robin. See Alon, Noga Tian, G. and Shing, Tung Yau. Complete Kahler manifolds with zero Ricci curvature. I, 579 Wahl, Jonathan. A characteristic number folinks ofsurface singularities, 625 Wilf, Herbert S. and Zeilberger, Domn. Rational junctions certify combinatorial identities, 147 Lin, Xiao-Song. See Habegger,Nathan Yang, Paul C. P. See Chang, Sun-Yung A. Zeilberger, Doron. See Wilf, Herbert S. ~"EM..tl'" ~~TO'~~: VOLUME 3 t~lMl~~------1-99-0------~ < "~'------",('o(;NDEO \'(1'"

AMERICAN MATHEMATICAL SOCIETY

EDITORS Michael Artin H. Blaine Lawson, Jr. Richard Melrose Wilfried Schmid Robert E. Tarjan

ASSOCIATE EDITORS James G. Arthur Peter Bickel Gerd Faltings Charles L. Fefferman Michael H. Freedman Daniel Friedan Ronald L. Graham Joe Harris Hendrik W. Lenstra, Jr. Andrew Majda Hugh L. Montgomery Paul H. Rabinowitz Karen Uhlenbeck W. Hugh Woodin

PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 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 a chapter 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, Rhode Island 02940.

Copyright © 1990 by the American Mathematical Society. All rights reserved. Printed in the United States of America The American Mathematical Society retains all rights except those granted to the United States Government. 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 AMS-TEX, the American Mathematical Society's TEX macro system. Journal of the American Mathematical Society

Volume 3, Number 1 January 1990

A partition property of simplices in Euclidean space P. FRANKL and V. RODL ......

The three-space problem for LI MICHEL T ALAGRAND ...... 9

Tight closure, invariant theory, and the Brian~on-Skoda Theorem MELVIN HOCHSTER and CRAIG HUNEKE...... 31

Isospectral conformal metrics on 3-manifolds SUN-YUNG A. CHANG and PAUL C. P. yANG...... 117

Rational functions certify combinatorial identities HERBERT S. WILF and DORON ZEILBERGER ...... 147

Koszul complexes, harmonic oscillators, and the Todd class JEAN-MICHEL BISMUT ...... 159

Finite dimensional Hopf algebras arising from Quantized universal en- veloping algebras GEORGE LuSZTIG...... 257

Volume 3, Number 2 April 1990

Efficient computation of the Fourier transform on finite groups PERSI DIACONIS and DANIEL ROCKMORE...... 297

Nodal sets for eigenfunctions of the Laplacian on surfaces HAROLD DONNELLY and CHARLES FEFFERMAN ...... 333

On complete manifolds with nonnegative Ricci curvature UWE ABRESCH and DETLEF GROMOLL...... 355

Inverse spectral results on two-dimensional tori V. GUILLEMIN...... 375 The classification of links up to link-homotopy NATHAN HABEGGER and XIAo-SONG LIN ...... 389

Kategorie ~, perverse Garben und Moduln tiber den Koinvarianten zur Weylgruppe WOLFGANG SOERGEL ...... 421

Canonical bases arising from quantized enveloping algebras G. LUSZTIG ...... 447

Volume 3, Number 3 July 1990

Horocyclic coordinates for Riemann surfaces and moduli spaces. I: Teichmtiller and Riemann spaces of Kleinian groups IRWIN KRA ...... 499

Complete Kahler manifolds with zero Ricci curvature. I G. TIAN and SHING TUNG YAU ...... 579

SU](2,F[z, liz)) for Fa subfield ofC DAVID POLLEN ...... :...... 611

A characteristic number for links of surface singularities JONATHAN WAHL...... 625

The intrinsic spread of a configuration in Rd JACOB E. GOODMAN, RICHARD POLLACK, and BERND STURMFELS.. 639

Euler's "Exemplum memorabile inductionis fallacis" and q-trinomial coefficients GEORGE E. ANDREWS...... 653

A pinching theorem for homotopy spheres KARSTEN GROVE and PETER PETERSEN V ...... 671

The structure of rational and ruled symplectic 4-manifolds DUSA McDuFF...... 679

Harmonic bundles on noncompact curves CARLOS T. SiMPSON...... 713 Volume 3, Number 4 October 1990

The n~-Singleton Conjecture SY D. FRIEDMAN ...... 771

Common range of co-analytic Toeplitz operators JOHN E. MCCARTHY...... 793

A separator theorem for nonplanar graphs NOGA ALON, PAUL SEYMOUR, and ROBIN THOMAS ...... 801

Embeddability for three-dimensional CR-manifolds DANIEL M. BURNS and CHARLES L. EpSTEIN ...... 809

Uniform tree lattices HYMAN BASS and RA VI KULKARNI...... 843

A Glimm-Effros dichotomy for Borel equivalence relations L. A. HARRINGTON, A. S. KECHRIS, and A. LOUVEAU ...... 903

Group representations and lattices BENEDICT H. GROSS ...... 929

Lattices of minimal covolume in SL2: a nonarchimedean analogue of Siegel's theorem J.l :2: 1C /21 ALEXANDER LUBOTZKY ...... 961 Manuscript submission. Manuscripts submitted for publication should either be typewritten double spaced or prepared using TEX and the JI,MS-TEX package. Two copies of the manuscript should be sent directly to one of the Editors. The signing of a Copyright Transfer Agreement is a requirement for publication. Subject classification. Included with the footnotes to the paper, but placed before the first footnote, the subject classification should represent the primary and secondary subjects of the article. A list may be found in the annual subject index of Mathematical Reviews, published with the December issue starting in 1984. Galley proof. When a paper with more than one author has been accepted for publication, only one set of proof will be sent. Joint authors should, therefore, indicate on the original manuscript which of them should receive galley proof in the event that the manuscript is accepted for publication. 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 acknowledgment 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 Executive Director, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940. ora fteAeia ahmtclSociety Mathematical American the of Journal JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 3, Number 4 October 1990

1 The Π2-Singleton Conjecture SY D.FRIEDMAN ...... 771

Common range of co-analytic Toeplitz operators JOHN E.MCCARTHY ...... 793

A separator theorem for nonplanar graphs NOGA ALON,PAUL SEYMOUR, and ROBIN THOMAS ...... 801

Embeddability for three-dimensional CR-manifolds DANIEL M.BURNS and CHARLES L.EPSTEIN ...... 809

Uniform tree lattices HYMAN BASS and RAVI KULKARNI ...... 843

A Glimm-Effros dichotomy for Borel equivalence relations L.A.HARRINGTON,A.S.KECHRIS, and A. LOUVEAU ...... 903

Group representations and lattices BENEDICT H.GROSS ...... 929 OUE3NME AE 7–7 COE 1990 OCTOBER 771–975 PAGES 4 NUMBER 3 VOLUME

Lattices of minimal covolume in SL2: a nonarchimedean analogue of Siegel’s theorem µ ≥ π/21 ALEXANDER LUBOTZKY ...... 961