Localized Index and $L^2$-Lefschetz fixed point formula for orbifolds

Abstract

We study a class of localized indices for the Dirac type operators on a complete Riemannian orbifold, where a discrete group acts properly, co-compactly and isometrically. These localized indices, generalizing the $L^2$-index of Atiyah, are obtained by taking certain traces of the higher index for the Dirac type operators along conjugacy classes of the discrete group. Applying the local index technique, we also obtain an $L^2$-version of the Lefschetz fixed point formula for orbifolds. These cohomological formulae for the localized indices give rise to a class of refined topological invariants for the quotient orbifold.

56 pages, submitted version

References in corpus (2)

• Geometrization of Three-Dimensional Orbifolds via Ricci Flow
• $L^2$-index formula for proper cocompact group actions

Cited by in corpus (1)

• Finiteness of fundamental groups