K theoretic virtual fundamental cycle of global Kuranishi chart

TL;DR

This paper introduces a new way to define the virtual fundamental cycle for global Kuranishi charts within the framework of orbifold K-homology, ensuring consistency with existing invariants.

Contribution

It formalizes the virtual fundamental cycle in the context of global Kuranishi charts and verifies its invariance with previous definitions.

Findings

Defines the virtual fundamental cycle in orbifold K-homology.

Proves the cycle yields the same invariants as prior methods.

Abstract

In this paper, we define the virtual fundamental cycle of a global Kuranishi chart as an element in the (analytic) orbispace K-homology of the virtual orbifold and verify that it defines the same invariants as those in \cite{Abouzaid23}.