Twisted K-theory and obstructions against positive scalar curvature metrics

Abstract

We decompose the twisted index obstruction $\theta (M)$ against positive scalar curvature metrics for oriented manifolds with spin universal cover into a pairing of a twisted $K$-homology with a twisted $K$-theory class and prove that $\theta (M)$ does not vanish if $M$ is an orientable enlargeable manifold with spin universal cover.

21 pages (drastically streamlined with focus on the proof of the non-vanishing result)

References in corpus (8)

• Twisted K-theory and K-theory of bundle gerbes
• A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture
• More Morphisms between Bundle Gerbes
• Enlargeability and index theory
• Enlargeability and index theory: Infinite covers
• Bundle Gerbes and Surface Holonomy
• Twisted K-theory, old and new
• Type I D-branes in an H-flux and twisted KO-theory

Cited by in corpus (1)

• The index of families of projective operators