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 of co-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............