scholarly journals The Local Index Formula in Noncommutative Geometry Revisited

2013 ◽  
Author(s):  
Alan L. Carey ◽  
John Phillips ◽  
Adam Rennie ◽  
Fedor A. Sukochev
Keyword(s):  
Noncommutative Geometry ◽  
Index Formula ◽  
Local Index

scholarly journals The local index formula in noncommutative geometry

1995 ◽  
Vol 5 (2) ◽  
pp. 174-243 ◽  
Author(s):  
A. Connes ◽  
H. Moscovici
Keyword(s):  
Noncommutative Geometry ◽  
Index Formula ◽  
Local Index

scholarly journals The local index formula in semifinite Von Neumann algebras I: Spectral flow

2006 ◽  
Vol 202 (2) ◽  
pp. 451-516 ◽  
Author(s):  
Alan L. Carey ◽  
John Phillips ◽  
Adam Rennie ◽  
Fyodor A. Sukochev
Keyword(s):  
Von Neumann Algebras ◽  
Index Formula ◽  
Spectral Flow ◽  
Local Index ◽  
Von Neumann

scholarly journals The local index formula in semifinite von Neumann algebras II: The even case

2006 ◽  
Vol 202 (2) ◽  
pp. 517-554 ◽  
Author(s):  
Alan L. Carey ◽  
John Phillips ◽  
Adam Rennie ◽  
Fyodor A. Sukochev
Keyword(s):  
Von Neumann Algebras ◽  
Index Formula ◽  
Local Index ◽  
Von Neumann

The local index formula for a Hermitian manifold

1997 ◽  
Vol 180 (1) ◽  
pp. 51-56
Author(s):  
Peter B. Gilkey ◽  
S. Nikčević ◽  
J. Pohjanpelto
Keyword(s):  
Hermitian Manifold ◽  
Index Formula ◽  
Local Index

An application to local index theory

2011 ◽  
Author(s):  
Jean-Michel Bismut
Keyword(s):  
Compact Manifold ◽  
Index Theory ◽  
Heat Kernels ◽  
Index Formula ◽  
Torsion Free Group ◽  
Local Index ◽  
Orbital Integrals ◽  
Index Formulas ◽  
Torsion Free

This chapter verifies the compatibility of the formula for the orbital integrals of heat kernels introduced in the previous chapter to the index formula of Atiyah-Singer, to the fixed point formulas of Atiyah-Bott, and to the index formula for orbifolds of Kawasaki. Given that the McKean-Singer formula expresses the index of a Dirac operator over a compact manifold Z as the supertrace of a heat kernel, if Z is the quotient of X by a cocompact torsion free group, this supertrace can be evaluated explicitly by the formulas provided in the previous chapter. This chapter directly checks these formulas to be compatible with the index formulas.

scholarly journals The Noncommutative Infinitesimal Equivariant Index Formula

2014 ◽  
Vol 14 (1) ◽  
pp. 73-102 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Heat Kernel ◽  
Explicit Formula ◽  
Noncommutative Geometry ◽  
Index Formula ◽  
Equivariant Index ◽  
Heat Kernel Asymptotics

AbstractIn this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regularity and give an explicit formula for them. We also establish an infinitesimal equivariant family index formula and introduce the infinitesimal equivariant eta forms as well as compare them with the equivariant eta forms.

scholarly journals A Local Index Formula for the Quantum Sphere

2004 ◽  
Vol 254 (2) ◽  
pp. 323-341 ◽  
Author(s):  
Sergey Neshveyev ◽  
Lars Tuset
Keyword(s):  
Index Formula ◽  
Local Index ◽  
Quantum Sphere
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