The Getzler calculus and the local index theorem

2013 ◽  
pp. 159-176
Keyword(s):  
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
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