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.
Publié le : 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, Tome 16 (2009) no. 1, pp. 647-664. http://gdmltest.u-ga.fr/item/1257776240/