Bordism Invariance of the Coarse Index

TL;DR

This paper proves that the coarse index of complex elliptic pseudodifferential operators remains invariant under bordism, with implications for the existence of positive scalar curvature metrics on open manifolds.

Contribution

It introduces directed c-bordisms and demonstrates their utility in establishing bordism invariance of the coarse index.

Findings

Coarse index is invariant under bordism.

Directed c-bordisms are useful tools in geometric analysis.

Results have implications for scalar curvature problems.

Abstract

We prove bordism invariance of the coarse index of complex elliptic pseudodifferential operators. In our discussion we introduce directed $c$-bordisms, whose usefulness is illustrated in the context of existence of uniformly positive scalar curvature metrics on open manifolds.