Rigidity and Vanishing Theorems in K-Theory II

TL;DR

This paper extends rigidity and vanishing theorems in K-theory to Spin^c manifolds, providing new results for families of almost complex manifolds and broadening the scope of previous theorems.

Contribution

It introduces a K-theory version of existing rigidity and vanishing theorems specifically for Spin^c cases and families of almost complex manifolds.

Findings

Established a K-theory version of rigidity theorems for Spin^c manifolds

Proved vanishing theorems for families of almost complex manifolds

Extended previous results to a broader class of geometric structures

Abstract

We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a family of almost complex manifolds.