Differential orbifold K-Theory

TL;DR

This paper develops a differential equivariant K-theory framework for smooth orbifolds, introducing push-forward maps and intersection pairings, extending the theory's applicability to orbifolds modeled as global quotients.

Contribution

It constructs a new differential equivariant K-theory for orbifolds, including push-forward maps and intersection pairings, expanding the tools available for orbifold topology.

Findings

Defines differential equivariant K-theory for orbifolds

Constructs push-forward maps for proper submersions

Establishes non-degenerate pairings in the theory

Abstract

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct a push-forward map in differential equivariant K-theory. Finally, we construct a non-degenerate intersection pairing with values in C/Z for the subclass of smooth orbifolds which can be written as global quotients by a finite group action. We construct a real subfunctor of our theory, where the pairing restricts to a non-degenerate R/Z-valued pairing.