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Type: Journal article
Title: Localized index and L2-lefschetz fixed-point formula for orbifolds
Author: Wang, B.
Wang, H.
Citation: Journal of Differential Geometry, 2016; 102(2):285-349
Publisher: International Press of Boston Inc.
Issue Date: 2016
ISSN: 0022-040X
Statement of
Bai-Ling Wang and Hang Wang
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, subject to some trace assumption. Applying the local index technique, we also obtain an L²-version of the Lefschetz fixed-point formulas for orbifolds. These cohomological formulas for the localized indices give rise to a class of refined topological invariants for the quotient orbifold.
DOI: 10.4310/jdg/1453910456
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