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

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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Cited by in corpus (3)

• Quotient Theorems in Polyfold Theory and $S^1$-Equivariant Transversality
• $T$-equivariant disc potentials for toric Calabi-Yau manifolds
• Monotone Lagrangian Floer theory in smooth divisor complements: I