VOLUME 19 NUMBER 4 OCTOBER 2006 J OOUF THE RNAL A M E R I C AN M A T H E M A T I C A L S O C I ET Y EDITORS Ingrid Daubechies Robert Lazarsfeld John W. Morgan Andrei Okounkov Terence Tao ASSOCIATE EDITORS Francis Bonahon Robert L. Bryant Weinan E Pavel I. Etingof Mark Goresky Alexander S. Kechris Robert Edward Kottwitz Peter Kronheimer Haynes R. Miller Andrew M. Odlyzko Bjorn Poonen Victor S. Reiner Oded Schramm Richard L. Taylor S. R. S. Varadhan Avi Wigderson Lai-Sang Young Shou-Wu Zhang PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 Available electronically at www.ams.org/jams/ 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. Submission information. See Information for Authors at the end of this issue. Publisher Item Identifier. The Publisher Item Identifier (PII) appears at the top of the first page of each article published in this journal. 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Printed in the United States of America. ∞ The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. 10987654321 111009080706 JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY CONTENTS Vol. 19, No. 4 October 2006 Soren Galatius, Ib Madsen, and Ulrike Tillmann, Divisibility of the stable Miller-Morita-Mumford classes ................................ 759 Nicolas Monod, Superrigidity for irreducible lattices and geometric splitting ................................................... 781 J. Krieger and W. Schlag, Stable manifolds for all monic supercritical focusing nonlinear Schr¨odingerequations in one dimension . 815 Nicole Lemire, Vladimir L. Popov, and Zinovy Reichstein, Cayley groups ................................................... 921 Charles Rezk, The units of a ring spectrum and a logarithmic cohomology operation ................................................... 969 INDEX TO VOLUME 19 (2006) Berrick, A. J., F. R. Cohen, Y. L. Wong, and J. Wu. Configurations, braids, and homotopy groups, 265 Braverman, M., and M. Yampolsky. Non-computable Julia sets, 551 Brenner, Holger, and Mordechai Katzman. On the arithmetic of tight closure, 659 Bufetov, Alexander I. Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichm¨uller flow on the moduli space of Abelian differentials, 579 Calegari, Danny, and David Gabai. Shrinkwrapping and the taming of hyperbolic 3-manifolds, 385 Cheeger, Jeff, and Gang Tian. Curvature and injectivity radius estimates for Einstein 4-manifolds, 487 Cohen, F. R. See Berrick, A. J. Deninger, Christopher. Fuglede–Kadison determinants and entropy for actions of discrete amenable groups, 737 Fintushel, Ronald, and Ronald J. Stern. Double node neighborhoods and families of simply con- nected 4-manifolds with b+ = 1, 171 Gabai, David. See Calegari, Danny Galatius, Soren, Ib Madsen, and Ulrike Tillmann. Divisibility of the stable Miller-Morita-Mumford classes, 759 Geisser, Thomas, and Lars Hesselholt. The de Rham-Witt complex and p-adic vanishing cycles, 1 Helfgott, H. A., and A. Venkatesh. Integral points on elliptic curves and 3-torsion in class groups, 527 Hesselholt, Lars. See Geisser, Thomas Ionescu, Alexandru D., and Stephen Wainger. Lp boundedness of discrete singular Radon trans- forms, 357 Jaikin-Zapirain, A. Zeta function of representations of compact p-adic analytic groups, 91 Katzman, Mordechai. See Brenner, Holger Krieger, J., and W. Schlag. Stable manifolds for all monic supercritical focusing nonlinear Schr¨odingerequations in one dimension, 815 Landsberg, J. M. The border rank of the multiplication of 2 × 2 matrices is seven, 447 Lauritzen, Niels, Ulf Raben-Pedersen, and Jesper Funch Thomsen. Global F -regularity of Schu- bert varieties with applications to D-modules, 345 Lemire, Nicole, Vladimir L. Popov, and Zinovy Reichstein. Cayley groups, 921 Li, Tao. Heegaard surfaces and measured laminations, II: Non-Haken 3–manifolds, 625 Liu, Chiu-Chu Melissa, and Shing-Tung Yau. Positivity of quasi-local mass II, 181 Madsen, Ib. See Galatius, Soren Markovic, Vladimir. Quasisymmetric groups, 673 Merle, Frank, and Pierre Raphael. On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schr¨odingerequation, 37 M¨oller,Martin. Variations of Hodge structures of a Teichm¨uller curve, 327 Monod, Nicolas. Superrigidity for irreducible lattices and geometric splitting, 781 Moore, Justin Tatch. A solution to the L space problem, 717 Popov, Vladimir L. See Lemire, Nicole Raben-Pedersen, Ulf. See Lauritzen, Niels Raphael, Pierre. See Merle, Frank Reichstein, Zinovy. See Lemire, Nicole Rezk, Charles. The units of a ring spectrum and a logarithmic cohomology operation, 969 Schlag, W. See Krieger, J. Sinha, Dev P. Operads and knot spaces, 461 Stern, Ronald J. See Fintushel, Ronald Szemer´edi,E., and V. Vu. Long arithmetic progressions in sumsets: Thresholds and bounds, 119 Thomsen, Jesper Funch. See Lauritzen, Niels Tian, Gang. See Cheeger, Jeff Tillmann, Ulrike. See Galatius, Soren Venkatesh, A. See Helfgott, H. A. Vu, V. See Szemer´edi,E. Wainger, Stephen. See Ionescu, Alexandru D. INDEX TO VOLUME 19 (2006) Wong, Y. L. See Berrick, A. J. Wu, J. See Berrick, A. J. Yampolsky, M. See Braverman, M. Yau, Shing-Tung. See Liu, Chiu-Chu Melissa Young, Matthew P. Low-lying zeros of families of elliptic curves, 205 Zlatoˇs,Andrej. Sharp transition between extinction and propagation of reaction, 251 VOLUME 19 2006 J OFO THE URNAL AMERICAN MATHEMATICAL SOCIETY EDITORS Ingrid Daubechies Robert Lazarsfeld John W. Morgan Andrei Okounkov Terence Tao ASSOCIATE EDITORS Francis Bonahon Robert L. Bryant Weinan E Pavel I. Etingof Mark Goresky Alexander S. Kechris Robert Edward Kottwitz Peter Kronheimer Haynes R. Miller Andrew M. Odlyzko Bjorn Poonen Victor S. Reiner Oded Schramm Richard L. Taylor S. R. S. Varadhan Avi Wigderson Lai-Sang Young Shou-Wu Zhang 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. Submission information. See Information for Authors at the end of this issue. Publisher