Volume 8, issue 2 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Real secondary index theory

Ulrich Bunke and Thomas Schick

Algebraic & Geometric Topology 8 (2008) 1093–1139
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 ĉk Hk1(B; ), certain secondary invariants.

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

Keywords
family index, secondary characteristic classes
Mathematical Subject Classification 2000
Primary: 57R20
References
Publication
Received: 12 July 2005
Revised: 23 May 2008
Accepted: 27 May 2008
Published: 6 July 2008
Authors
Ulrich Bunke
Universität Regensburg
Mathematische Fakultät
93040 Regensburg
Germany
http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/Bunke
Thomas Schick
Georg-August-Universität Göttingen
Mathematisches Institut
Bunsenstr. 3
37073 Göttingen
Germany
http://www.uni-math.gwdg.de/schick