Volume 157 Issue 2 – March 2003

## Homotopy hyperbolic 3-manifolds are hyperbolic

Pages 335-431 by David Gabai, G. Robert Meyerhoff, Nathaniel Thurston | From volume 157-2

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

Pages 433-519 by Tim D. Cochran, Kent E. Orr, Peter Teichner | From volume 157-2

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

Pages 521-544 by Huaxin Lin | From volume 157-2

## On a coloring conjecture about unit fractions

Pages 545-556 by Ernest S. Croot, III | From volume 157-2

## Convergence or generic divergence of the Birkhoff normal form

Pages 557-574 by Ricardo Pérez-Marco | From volume 157-2

## Integrability of Lie brackets

Pages 575-620 by Marius Crainic, Rui Loja Fernandes | From volume 157-2

## Subvarieties of Shimura varieties

Pages 621-645 by Bas Edixhoven, Andrei Yafaev | From volume 157-2

## The best constant for centered Hardy-Littlewood maximal inequality

Pages 647-688 by Antonios D. Melas | From volume 157-2

## New upper bounds on sphere packings I

Pages 689-714 by Henry Cohn, Noam Elkies | From volume 157-2