Hypertoric manifolds and hyperKähler moment maps

Author: 

Dancer, A
Swann, A

Publication Date: 

1 September 2017

Journal: 

New Perspectives in Differential Geometry: Special Metrics and Quaternionic Geometry

Last Updated: 

2020-01-31T12:21:53.933+00:00

DOI: 

10.1007/978-3-319-67519-0_5

abstract: 

We discuss various aspects of moment map geometry in symplectic and hyperKähler geometry. In particular, we classify complete hyperKähler manifolds of dimension 4n with a tri-Hamiltonian action of a torus of dimension n, without any assumption on the finiteness of the Betti numbers. As a result we find that the hyperKähler moment in these cases has connected fibres, a property that is true for symplectic moment maps, and is surjective. New examples of hypertoric manifolds of infinite topological type are produced. We provide examples of non-Abelian triHamiltonian group actions of connected groups on complete hyperKähler manifolds such that the hyperKähler moment map is not surjective and has some fibres that are not connected. We also discuss relationships to symplectic cuts, hyperKähler modifications and implosion constructions.

Symplectic id: 

653586

Submitted to ORA: 

Submitted

Publication Type: 

Conference Paper