Volume 18, issue 2 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Classification of Hamiltonian torus actions with two-dimensional quotients

Yael Karshon and Susan Tolman

Geometry & Topology 18 (2014) 669–716
Abstract

We construct all possible Hamiltonian torus actions for which all the nonempty reduced spaces are two-dimensional (and not single points) and the manifold is connected and compact, or, more generally, the moment map is proper as a map to a convex set. This construction completes the classification of tall complexity-one spaces.

Keywords
Hamiltonian torus action, symplectic geometry, momentum map, moment map
Mathematical Subject Classification 2010
Primary: 53D35
Secondary: 53D20, 57S15, 52B20, 14M25
References
Publication
Received: 9 May 2012
Revised: 23 February 2013
Accepted: 9 April 2013
Published: 20 March 2014
Proposed: Frances Kirwan
Seconded: Leonid Polterovich, Richard Thomas
Authors
Yael Karshon
Department of Mathematics
University of Toronto
40st George Street
6th floor
Toronto, ON M5S 2E4
Canada
http://www.math.toronto.edu/karshon
Susan Tolman
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana, IL 61801
USA
http://www.math.uiuc.edu/~stolman