Journal of Differential Geometry

The transverse index theorem for proper cocompact actions of Lie groupoids

Markus J. Pflaum, Hessel Posthuma, and Xiang Tang

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Abstract

Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples the meaning of the index pairing and our index formula.

Article information

Source
J. Differential Geom., Volume 99, Number 3 (2015), 443-472.

Dates
First available in Project Euclid: 25 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1424880982

Digital Object Identifier
doi:10.4310/jdg/1424880982

Mathematical Reviews number (MathSciNet)
MR3316973

Zentralblatt MATH identifier
1328.58017

Citation

Pflaum, Markus J.; Posthuma, Hessel; Tang, Xiang. The transverse index theorem for proper cocompact actions of Lie groupoids. J. Differential Geom. 99 (2015), no. 3, 443--472. doi:10.4310/jdg/1424880982. https://projecteuclid.org/euclid.jdg/1424880982


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Lehigh University

International Press

Journal of Differential Geometry

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