Geodesic
Real secondary index theory
Bunke, Ulrich1 ; Schick, Thomas2
1Universität Regensburg, Mathematische Fakultät, 93040 Regensburg, Germany
2Georg-August-Universität Göttingen, Mathematisches Institut, Bunsenstr. 3, 37073 Göttingen, Germany
Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1093-1139
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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 ∈ Hk−1(B; ℝ∕ℤ), certain secondary invariants.

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

DOI : 10.2140/agt.2008.8.1093
Keywords: family index, secondary characteristic classes

Bunke, Ulrich  1   ; Schick, Thomas  2

1 Universität Regensburg, Mathematische Fakultät, 93040 Regensburg, Germany
2 Georg-August-Universität Göttingen, Mathematisches Institut, Bunsenstr. 3, 37073 Göttingen, Germany 
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Bunke, Ulrich; Schick, Thomas. Real secondary index theory. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1093-1139. doi: 10.2140/agt.2008.8.1093

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