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The spectral flow of the odd signature operator and higher Massey products

Published online by Cambridge University Press:  01 March 1997

PAUL A. KIRK  and
ERIC P. KLASSEN
PAUL A. KIRK
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
ERIC P. KLASSEN
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, U.S.A.
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Abstract

Given an analytic path of flat connections on a principal U(N)-bundle over a closed odd-dimensional manifold M, how can we calculate the spectral flow of the corresponding path Dt of signature operators on an associated vector bundle E → M? In this paper we give an algebraic-topological answer to this question in terms of cohomology, cup products and higher Massey products.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 2 , March 1997 , pp. 297 - 320
Copyright
© Cambridge Philosophical Society 1997

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