Heat-Kernel Asymptotics of Locally Symmetric Spaces of Rank One and Chern-Simons Invariants

TL;DR

This paper studies the heat kernel asymptotics on rank one locally symmetric spaces and derives Chern-Simons invariants for flat connections on hyperbolic 3-manifolds, linking geometric analysis with topological invariants.

Contribution

It provides new asymptotic expansions for heat kernels on rank one symmetric spaces and computes Chern-Simons invariants for irreducible flat connections on hyperbolic 3-manifolds.

Findings

Asymptotic expansion formulas for heat kernels on rank one spaces

Explicit Chern-Simons invariants for flat connections on hyperbolic 3-manifolds

Connections between spectral geometry and topological invariants

Abstract

The asymptotic expansion of the heat kernel associated with Laplace operators is considered for general irreducible rank one locally symmetric spaces. Invariants of the Chern-Simons theory of irreducible U(n)- flat connections on real compact hyperbolic 3-manifolds are derived