Fukaya's conjecture on $S^1$-equivariant de Rham complex

Abstract

Getzler-Jones-Petrack introduced $A_{\infty }$ structures on the equivariant complex for manifold $M$ with smooth ${\mathbb{S}}^1$ action, motivated by geometry of loop spaces. Applying Witten's deformation by Morse functions followed by homological perturbation we obtained a new set of $A_{\infty }$ structures. We extend and prove Fukaya's conjecture relating this Witten's deformed equivariant de Rham complexes, to a new Morse theoretical $A_{\infty }$ complexes defined by counting gradient trees with jumping which are closely related to the ${\mathbb{S}}^1$ equivariant symplectic cohomology proposed by Siedel.

18 pages, 4 figures

References in corpus (1)

• S^1-equivariant Morse cohomology