ETA AND RHO INVARIANTS ON MANIFOLDS WITH EDGES

被引：7

作者：

Piazza, Paolo ^{[1
]}

Vertman, Boris ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Matemat, Rome, Italy

[2] Carl von Ossietzky Univ Oldenburg, Inst Math, Oldenburg, Germany

来源：

ANNALES DE L INSTITUT FOURIER | 2019年 / 69卷 / 05期

关键词：

stratified space; incomplete edge metrics; spin manifold; signature operator; spin Dirac operator; heat kernel asymptotic; eta invariant; rho invariant; Fredholm index; SPECTRAL ASYMMETRY; CONICAL SINGULARITIES; ANALYTIC-TORSION; FAMILIES INDEX; BOUNDARY; THEOREM; OPERATOR; SUPERCONNECTIONS; L(2)-TORSION; ASYMPTOTICS;

D O I：

10.5802/aif.3287

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish existence of eta-invariants as well as of the Atiyah-Patodi-Singer and the Cheeger-Gromov rho-invariants for a class of Dirac operators on an incomplete edge space. Our analysis applies in particular to the signature and the spin Dirac operator. We derive an analogue of the Atiyah-Patodi-Singer index theorem for incomplete edge spaces and their non-compact infinite Galois coverings with edge singular boundary. Our arguments are based on the microlocal analysis of the heat kernel asymptotics associated to the Dirac laplacian of an incomplete edge metric. As an application, we discuss stability results for the two rho-invariants we have defined.

引用

页码：1955 / 2035

页数：81

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