Local index theorem for Dirac operator

1987 ◽  
Vol 3 (2) ◽  
pp. 152-169 ◽  
Author(s):  
Yu Yanlin
Keyword(s):  
Dirac Operator ◽  
Index Theorem ◽  
Local Index ◽  
Local Index Theorem

A local index theorem for non K�hler manifolds

1989 ◽  
Vol 284 (4) ◽  
pp. 681-699 ◽  
Author(s):  
Jean-Michel Bismut
Keyword(s):  
Index Theorem ◽  
Local Index ◽  
Local Index Theorem

scholarly journals Local index theorem for families.

1988 ◽  
Vol 35 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Harold Donnelly
Keyword(s):  
Index Theorem ◽  
Local Index ◽  
Local Index Theorem

NONUNITAL SPECTRAL TRIPLES ASSOCIATED TO DEGENERATE METRICS

2004 ◽  
Vol 16 (01) ◽  
pp. 125-146
Author(s):  
A. RENNIE
Keyword(s):  
Finite Dimension ◽  
Index Theorem ◽  
Smooth Manifolds ◽  
Spectral Triples ◽  
Local Index ◽  
Dimension Spectrum ◽  
Spectrum Hypothesis ◽  
Local Index Theorem ◽  
K Theory

We show that one can define (p,∞)-summable spectral triples using degenerate metrics on smooth manifolds. Furthermore, these triples satisfy Connes–Moscovici's discrete and finite dimension spectrum hypothesis, allowing one to use the Local Index Theorem [1] to compute the pairing with K-theory. We demonstrate this with a concrete example.

scholarly journals Local index theorem for orbifold Riemann surfaces

2018 ◽  
Vol 109 (5) ◽  
pp. 1119-1143 ◽  
Author(s):  
Leon A. Takhtajan ◽  
Peter Zograf
Keyword(s):  
Riemann Surfaces ◽  
Index Theorem ◽  
Local Index ◽  
Local Index Theorem

scholarly journals Local index theory and the Riemann–Roch–Grothendieck theorem for complex flat vector bundles

2018 ◽  
Vol 12 (04) ◽  
pp. 941-987
Author(s):  
Man-Ho Ho
Keyword(s):  
Vector Bundle ◽  
Dirac Operator ◽  
Differential Form ◽  
Vector Bundles ◽  
Variational Formula ◽  
Index Theory ◽  
Index Theorem ◽  
Local Index ◽  
Chern Simons ◽  
Local Family

The purpose of this paper is to give a proof of the real part of the Riemann–Roch–Grothendieck theorem for complex flat vector bundles at the differential form level in the even dimensional fiber case. The proof is, roughly speaking, an application of the local family index theorem for a perturbed twisted spin Dirac operator, a variational formula of the Bismut–Cheeger eta form without the kernel bundle assumption in the even dimensional fiber case, and some properties of the Cheeger–Chern–Simons class of complex flat vector bundle.

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