Journal of Differential Geometry

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

Bai-Ling Wang and Hang Wang

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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, subject to some trace assumption. Applying the local index technique, we also obtain an $L^2$-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.

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J. Differential Geom., Volume 102, Number 2 (2016), 285-349.

First available in Project Euclid: 27 January 2016

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Wang, Bai-Ling; Wang, Hang. Localized index and $L^2$-Lefschetz fixed-point formula for orbifolds. J. Differential Geom. 102 (2016), no. 2, 285--349. doi:10.4310/jdg/1453910456.

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