New index formulas as a meromorphic generalization of the Chern-Gauss-Bonnet theorem
High Energy Physics - Theory
2008-02-03 v1 funct-an
General Relativity and Quantum Cosmology
Functional Analysis
Abstract
Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a result two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated type Klein) surfaces are derived.
Keywords
Cite
@article{arxiv.hep-th/9607209,
title = {New index formulas as a meromorphic generalization of the Chern-Gauss-Bonnet theorem},
author = {N. V. Borisov and Kirill Ilinski and Gleb Kalinin},
journal= {arXiv preprint arXiv:hep-th/9607209},
year = {2008}
}
Comments
LATEX, 14 pages