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arXiv · 1701.02840

Lie groupoid, deformation of unstable curve, and construction of equivariant Kuranishi charts

Kenji Fukaya
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Abstract

In this paper we give detailed construction of $G$-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 {\it unstable} marked curves using the language of Lie groupoid (which is {\it not} necessary etale) and the Riemannnian center of mass technique. This proof is actually similar to [FOn,Sections 13 and 15] except the usage of the language of Lie groupoid makes the argument more transparent. This version correct some errors of the previous version especially those pointed out by the referee.

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Kenji Fukaya. 2017-01-11. Lie groupoid, deformation of unstable curve, and construction of equivariant Kuranishi charts. https://arxiv.org/abs/1701.02840

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