Eta Invariants for Even Dimensional Manifolds

2011/10/13 by Xianzhe Dai, Dai, Xianzhe
Mathematics · #58Jxx #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:58Jxx

paper · pdf · doi:10.48550/arxiv.1110.3063

to appear in Proceedings of the fifth ICCM

arxiv created 2011/10/13 · arxiv updated 2011/10/17

Abstract

In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to K¹ representatives on even dimensional manifolds, and is defined on a finite cylinder, rather than on the manifold itself. Thus it is an interesting question to find an intrinsic spectral interpretation of this new invariant. Using adiabatic limit technique, we give such an intrinsic interpretation.

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