Heat equation approach to index theorems on odd dimensional manifolds
Zadeh, Mostafa Esfahani
Bull. Belg. Math. Soc. Simon Stevin, Volume 16 (2009) no. 1, p. 647-664 / Harvested from Project Euclid
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The subject of this paper is the index theorem on odd-dimensional manifolds with boundary. Such a theorem has been formulated and proved by D. Freed and his proof is based on analysis by Calderon and Seeley. In this paper we prove this theorem using the heat kernel methods for boundary conditions of Dirichlet and Neumann type. Moreover, we also consider the Atiyah-Patodi-Singer spectral boundary condition which is not studied in Freed's paper. As a direct consequence of the method, we obtain some information about isospectral invariants of the boundary conditions. This proof does not use the cobordism invariance of the index and is generalized easily to the family case.
Published online : 2009-11-15
Classification:  Dirac operators,  index theory,  Heat operator,  local and global boundary conditions,  58G10 
@article{1257776240,
     author = {Zadeh, Mostafa Esfahani},
     title = {Heat equation approach to index theorems on odd dimensional manifolds},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 647-664},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257776240}
}

Zadeh, Mostafa Esfahani. Heat equation approach to index theorems on odd dimensional manifolds. Bull. Belg. Math. Soc. Simon Stevin, Volume 16 (2009) no. 1, pp.  647-664. http://gdmltest.u-ga.fr/item/1257776240/