Adiabatic limit of the eta invariant over cofinite quotient of PSL(2,R)

TL;DR

This paper investigates the behavior of the eta invariant of the Dirac operator in the adiabatic limit on a noncompact manifold formed by a cofinite quotient of PSL(2,R), focusing on the effects of a fibred-cusp metric.

Contribution

It provides a detailed analysis of the eta invariant's adiabatic limit on noncompact, fibred-cusp manifolds derived from PSL(2,R) quotients, a novel setting in spectral geometry.

Findings

Characterization of the eta invariant's limit behavior

Insights into spectral properties of Dirac operators on noncompact manifolds

Extension of adiabatic limit techniques to fibred-cusp geometries

Abstract

We study the adiabatic limit of the eta invariant of the Dirac operator over cofinite quotient of PSL(2,R), which is a noncompact manifold with a nonexact fibred-cusp metric near the ends.