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Hamiltonian circle action with self-indexing moment map

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Title
Hamiltonian circle action with self-indexing moment map
Author(s)
Yunhyung Cho; Kim M.K.
Publication Date
2016-07
Journal
MATHEMATICAL RESEARCH LETTERS, v.23, no.3, pp.719 - 732
Publisher
INT PRESS BOSTON
Abstract
Let (M,ω) be a 2n-dimensional closed symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points, and let μ : M → ℝ be a moment map. Then it is well-known that μ is a Morse function whose critical point set coincides with the fixed point set MS1. Let ∧2k be the set of all fixed points of Morse index 2k. In this paper, we will show that if μ is constant on ∧2k for each k ≤ n, then (M,ω) satisfies the hard Lefschetz property. In particular, if (M,ω) admits a self-indexing moment map, i.e. μ(z) = 2k for every k ≤ n and z ∈∧2k, then (M,ω) satisfies the hard Lefschetz property
URI
https://pr.ibs.re.kr/handle/8788114/2831
ISSN
1073-2780
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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