Combinatorial heat kernels and L('2)-topological invariants

Gabor Elek, Purdue University

Abstract

We investigate the geometry of the combinatorial Laplacian and the combinatorial heat kernels on infinite simplicial complexes. First of all, we prove the combinatorial analog of Atiyah's $L\sp2$-index theorem and Roe's index theorem on open manifolds. Then we generalize the Kazhdan-Gromov inequality and obtain a new proof of Luck's theorem for Abelian groups. Finally, we prove that the $L\sp2$-Reidemeister-Franz torsion of a cyclic covering is always an algebraic number. (8), (9), (10).

Degree

Ph.D.

Advisors

Donnelly, Purdue University.

Subject Area

Mathematics

COinS