Twisted K-theory and obstructions against positive scalar curvature metrics

Details Twisted K-theory and obstructions against positive scalar curvature metrics Twisted K-theory and obstructions against positive scalar curvature metrics

2011-08-18

arxiv.org/abs/1108.3701v2

Mathematics

Geometric Topology

53 pages (minor changes to the references)

Scientific paper

Motivated by the index obstruction \theta(M) to positive scalar curvature metrics as defined in the untwisted case by Rosenberg and in the twisted case by Stolz, we develop twisted K-theory with coefficients in a C*-algebra A in terms of twisted Hilbert A-module bundles. We then decompose \theta(M) as 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, where the covers in the definition of enlargeability may have infinite numbers of leafs.

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