Secondary Invariants for String Bordism and tmf

Abstract

Using spectral invariants of Dirac operators we construct a secondary version of the Witten genus, a bordism invariant of string manifolds in dimensions $4m-1$. We prove a secondary index theorem which relates this global-analytic construction with its homotopy-theoretic analog. The latter will be calculated through its factorization over topological modular forms.

56 pages, 2 pictures

Cited by in corpus (2)

• Differential K-theory. A survey
• M-Theory with Framed Corners and Tertiary Index Invariants