The equivariant cohomology of complexity one spaces

Tara S. Holm; Liat Kessler

The equivariant cohomology of complexity one spaces

Symplectic Geometry 2019-10-10 v2

Authors: Tara S. Holm , Liat Kessler

Abstract

Complexity one spaces are an important class of examples in symplectic geometry. Karshon and Tolman classify them in terms of combinatorial and topological data. In this paper, we compute the equivariant cohomology for any complexity one space $T^{n-1}$ acting on $M^{2n}$ . The key step is to compute the equivariant cohomology for any Hamiltonian $S^1$ action on $M^4$ .

Keywords

symplectic geometry equivariant cohomology complexity one spaces Hamiltonian S^1 action torus actions classification

Cite

@article{arxiv.1512.09297,
  title  = {The equivariant cohomology of complexity one spaces},
  author = {Tara S. Holm and Liat Kessler},
  journal= {arXiv preprint arXiv:1512.09297},
  year   = {2019}
}

Comments

25 pages, 3 figures, 1 table. Third version incorporates clarifications of how the results differ from those already in the literature

The equivariant cohomology of complexity one spaces

Abstract

Keywords

Cite

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