2019/01/28 by Ma, Ziming Nikolas
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1901.09708
Getzler-Jones-Petrack introduced A_∞ structures on the equivariant complex for manifold M with smooth \mathbbS1 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_∞ structures. We extend and prove Fukaya's conjecture relating this Witten's deformed equivariant de Rham complexes, to a new Morse theoretical A_∞ complexes defined by counting gradient trees with jumping which are closely related to the \mathbbS1 equivariant symplectic cohomology proposed by Siedel.