scholarly journals An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary

1997 ◽  
Vol 46 (2) ◽  
pp. 287-334 ◽  
Author(s):  
Richard B. Melrose ◽  
Paolo Piazza
Keyword(s):  
Dirac Operators ◽  
Index Theorem ◽  
Manifolds With Boundary

scholarly journals An L2-Index Theorem for Dirac Operators on S1×R3

2000 ◽  
Vol 177 (1) ◽  
pp. 203-218 ◽  
Author(s):  
Tom M.W. Nye ◽  
Michael A. Singer
Keyword(s):  
Dirac Operators ◽  
Index Theorem ◽  
L2 Index

Twisted dirac operators and Kastler-Kalau-Walze theorems for six-dimensional manifolds with boundary

2020 ◽  
Vol 17 (14) ◽  
pp. 2050211
Author(s):  
Sining Wei ◽  
Yong Wang
Keyword(s):  
Vector Bundle ◽  
Dirac Operators ◽  
Manifolds With Boundary ◽  
Unitary Connection ◽  
Twisted Dirac Operators

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.

scholarly journals An index theorem for manifolds with boundary

2009 ◽  
Vol 347 (23-24) ◽  
pp. 1393-1398 ◽  
Author(s):  
Paulo Carrillo-Rouse ◽  
Bertrand Monthubert
Keyword(s):  
Index Theorem ◽  
Manifolds With Boundary

scholarly journals A Kastler-Kalau-Walze Type Theorem and the Spectral Action for Perturbations of Dirac Operators on Manifolds with Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Type Theorem ◽  
Dirac Operators ◽  
Compact Manifolds ◽  
Manifolds With Boundary ◽  
Spectral Action ◽  
Gravitational Action

We prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with two-form perturbations on 4-dimensional compact manifolds.

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