Relative Index Pairing and Odd Index Theorem for Even Dimensional Manifolds

2010/01/27 by Zhizhang Xie, Xie, Zhizhang
Mathematics · #46L80 #58Jxx #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.DG #math.KT #msc:46L80 #msc:58Jxx

paper · pdf · doi:10.48550/arxiv.1001.4822

19 pages

openalex publication_date 2010/01/27 · arxiv created 2010/10/12 · arxiv updated 2010/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an analogue for even dimensional manifolds of the Atiyah-Patodi-Singer twisted index theorem for trivialized flat bundles. We show that the eta invariant appearing in this result coincides with the eta invariant by Dai and Zhang up to an integer. We also obtain the odd dimensional counterpart for manifolds with boundary of the relative index pairing by Lesch, Moscovici and Pflaum.

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