Volume 18, issue 2 (2014)

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Classification of Hamiltonian torus actions with two-dimensional quotients

Yael Karshon and Susan Tolman

Geometry & Topology 18 (2014) 669–716

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.

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