Volume 157 Issue 2 – March 2003

Homotopy hyperbolic 3-manifolds are hyperbolic

Pages 335-431 by David Gabai, G. Robert Meyerhoff, Nathaniel Thurston

Knot concordance, Whitney towers and $L^2$-signatures

Pages 433-519 by Tim D. Cochran, Kent E. Orr, Peter Teichner

Classification of simple $C^{*}$-algebras and higher dimensional noncommutative tori

Pages 521-544 by Huaxin Lin

On a coloring conjecture about unit fractions

Pages 545-556 by Ernest S. Croot, III

Convergence or generic divergence of the Birkhoff normal form

Pages 557-574 by Ricardo Pérez-Marco

Integrability of Lie brackets

Pages 575-620 by Marius Crainic, Rui Loja Fernandes

Subvarieties of Shimura varieties

Pages 621-645 by Bas Edixhoven, Andrei Yafaev

The best constant for centered Hardy-Littlewood maximal inequality

Pages 647-688 by Antonios D. Melas

New upper bounds on sphere packings I

Pages 689-714 by Henry Cohn, Noam Elkies