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2008 Real secondary index theory
Ulrich Bunke, Thomas Schick
Algebr. Geom. Topol. 8(2): 1093-1139 (2008). DOI: 10.2140/agt.2008.8.1093

Abstract

In this paper, we study the family index of a family of spin manifolds. In particular, we discuss to what extent the real index (of the Dirac operator of the real spinor bundle if the fiber dimension is divisible by 8) which can be defined in this case contains extra information over the complex index (the index of its complexification). We study this question under the additional assumption that the complex index vanishes on the k–skeleton of B. In this case, we define new analytical invariants ĉkHk1(B;), certain secondary invariants.

We give interesting nontrivial examples. We then describe this invariant in terms of known topological characteristic classes.

Citation

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Ulrich Bunke. Thomas Schick. "Real secondary index theory." Algebr. Geom. Topol. 8 (2) 1093 - 1139, 2008. https://doi.org/10.2140/agt.2008.8.1093

Information

Received: 12 July 2005; Revised: 23 May 2008; Accepted: 27 May 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1157.57018
MathSciNet: MR2443109
Digital Object Identifier: 10.2140/agt.2008.8.1093

Subjects:
Primary: 57R20

Rights: Copyright © 2008 Mathematical Sciences Publishers

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