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The Fundamental Group of S1-manifolds

Published online by Cambridge University Press:  20 November 2018

Leonor Godinho  and
M. E. Sousa-Dias
Leonor Godinho*
Affiliation:
Departmento de Matem´atica, Instituto Superior T´ecnico, Lisbon, Portugal
*
lgodin@math.ist.utl.pt
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Abstract

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We address the problem of computing the fundamental group of a symplectic ${{S}^{1}}$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian ${{S}^{1}}$-action. Several examples are presented to illustrate our main results.

Keywords

53D2037J1055Q05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 5 , 01 October 2010 , pp. 1082 - 1098
Copyright
Copyright © Canadian Mathematical Society 2010

Footnotes

Both authors were partially supported by FCT through program POCTI/FEDER; the first author was partially supported by FCT through grant POCTI/MAT/57888/2004 and by Fundação Calouste Gulbenkian

1

This generalized moment map is a special case of a Lie group-valued moment map (see [OR] and the references therein).

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