Classification of momentum proper exact Hamiltonian group actions and the equivariant Eliashberg cotangent bundle conjecture-Reference-Cited by-同舟云学术

Classification of momentum proper exact Hamiltonian group actions and the equivariant Eliashberg cotangent bundle conjecture

Published:2023-09-27 Issue:5 Volume:29 Page:
ISSN:1022-1824
Container-title:Selecta Mathematica
language:en
Short-container-title:Sel. Math. New Ser.

Author:

Ziltener Fabian

Abstract

AbstractLet G be a compact and connected Lie group. The Hamiltonian G-model functor maps the category of symplectic representations of closed subgroups of G to the category of exact Hamiltonian G-actions. Based on previous joint work with Y. Karshon, the restriction of this functor to the momentum proper subcategory on either side induces a bijection between the sets of isomorphism classes. This classifies all momentum proper exact Hamiltonian G-actions (of arbitrary complexity). As an extreme case, we obtain a version of the Eliashberg cotangent bundle conjecture for transitive smooth actions. As another extreme case, the momentum proper Hamiltonian G-actions on contractible manifolds are exactly the symplectic G-representations, up to isomorphism.

Funder

Swiss Federal Institute of Technology Zurich

Publisher

Springer Science and Business Media LLC

Subject

General Physics and Astronomy,General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00029-023-00871-w.pdf

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