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Lie Groupoids, Deformation of Unstable Curves, and Construction of Equivariant Kuranishi Charts

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Title
Lie Groupoids, Deformation of Unstable Curves, and Construction of Equivariant Kuranishi Charts
Author(s)
Kenji Fukaya
Publication Date
2021
Journal
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, v.57, no.3-4, pp.1109 - 1225
Publisher
KYOTO UNIV, PUBLICATIONS RESEARCH INST MATHEMATICAL SCIENCES
Abstract
In this paper we give the detailed construction of a G-equivariant Kuranishi chart of moduli spaces of pseudo-holomorphic curves to a symplectic manifold with G-action, for an arbitrary compact Lie group G. The proof is based on the deformation theory of unstable marked curves using the language of Lie groupoids (which is not necessarily etale) and the Riemannian center of mass technique. This proof is actually similar to Fukaya and Ono (Arnold conjecture and Gromov-Witten invariant, Topology 38 (1999), 933-1048, Sects. 13 and 15), except that the usage of the language of Lie groupoids makes the argument more transparent.
URI
https://pr.ibs.re.kr/handle/8788114/10925
DOI
10.4171/PRIMS/57-3-13
ISSN
0034-5318
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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