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Combinatorial Heat Kernels and Index Theorems

✍ Scribed by G. Elek

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
398 KB
Volume
129
Category
Article
ISSN
0022-1236

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✦ Synopsis

In this paper we give a local heat kernel proof for the combinatorial (I)-index theorem and the (\Gamma)-Lefschetz theorem. We also use this method to prove the combinatorial version of Roe's index theorem on open manifolds. "1995 Academic Press. Inc

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We consider the challenging problem of Chavel's conjecture on the domain monotonicity of the fundamental solution of the Neumann problem. It says that if \(D \subset \tilde{D}\) are open convex domains and if \(p_{t}(x, y)\) and \(\tilde{p}_{t}(x, y)\) denote the corresponding parabolic heat kernels