Volume 171 Issue 1 – January 2010

## The classification of Kleinian surface groups, I: models and bounds

Pages 1-107 by Yair Minsky | From volume 171-1

## Uniqueness for the signature of a path of bounded variation and the reduced path group

Pages 109-167 by Ben Hambly, Terry Lyons | From volume 171-1

## Transformations of elliptic hypergeometric integrals

Pages 169-243 by Eric M. Rains | From volume 171-1

## Mirković-Vilonen cycles and polytopes

Pages 245-294 by Joel Kamnitzer | From volume 171-1

## Noise stability of functions with low influences: Invariance and optimality

Pages 295-341 by Elchanan Mossel, Ryan O’Donnell, Krzysztof Oleszkiewicz | From volume 171-1

## Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces

Pages 343-373 by Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann | From volume 171-1

## On the classification of finite-dimensional pointed Hopf algebras

Pages 375-417 by Nicolás Andruskiewitsch , Hans-Jürgen Schneider | From volume 171-1

## Dyson’s ranks and Maass forms

Pages 419-449 by Kathrin Bringmann, Ken Ono | From volume 171-1

## On the ergodicity of partially hyperbolic systems

Pages 451-489 by Keith Burns, Amie Wilkinson | From volume 171-1

## The Smith-Toda complex $V((p+1)/2)$ does not exist

Pages 491-509 by Lee S. Nave | From volume 171-1

## The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields

Pages 511-532 by Bjorn Poonen, José Felipe Voloch | From volume 171-1

## Essential dimension, spinor groups, and quadratic forms

Pages 533-544 by Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli | From volume 171-1

## Pentagon and hexagon equations

Pages 545-556 by Hidekazu Furusho | From volume 171-1

## A nonhomogeneous orbit closure of a diagonal subgroup

Pages 557-570 by François Maucourant | From volume 171-1

## Tight closure does not commute with localization

Pages 571-588 by Holger Brenner, Paul Monsky | From volume 171-1

## Characterization of Lee-Yang polynomials

Pages 589-603 by David Ruelle | From volume 171-1

## Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet)

Pages 605-618 by Andrew Hassell, Luc Hillairet | From volume 171-1