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Secondary invariants for string cobordism and tmf

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Bunke, Ulrich ; Naumann, Niko
Date of publication of this fulltext: 19 Jul 2010 08:49


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.

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