Secondary invariants for string bordism and topological modular forms

Abstract

Using spectral invariants of Dirac operators we construct a secondary version of the Witten genus, namely 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. (C) 2014 Elsevier Masson SAS. All rights reserved.