Localized Index and L²-Lefschetz fixed point formula for orbifolds

2013/07/08 by Wang, Bai-Ling, Wang, Hang
#Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1307.2088

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 L²-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 L²-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.

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