Equivariant K-theory and Resolution I: Abelian Actions
Name
1807.08299.pdf
Description
Submitted version
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249.24 KB
Format
Adobe PDF
Checksum (MD5)
5a66ae8332a4dab6633e5e604fe213db
Author(s)
Dimakis, P
Melrose, R
Date Issued
2020
Publisher
Springer International Publishing
Citation
Dimakis, P and Melrose, R. 2020. "Equivariant K-theory and Resolution I: Abelian Actions." 333.
Version
Original manuscript
Abstract
© 2020, Springer Nature Switzerland AG. The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type, in an iterated sense, with connecting fibrations and this structure descends to a resolution of the quotient. For an Abelian group action the equivariant K-theory can then be described in terms of bundles over the base with morphisms covering the connecting maps. A similar model is given, in terms of appropriately twisted deRham forms over the base as an iterated space, for delocalized equivariant cohomology in the sense of Baum, Brylinski and MacPherson. This approach allows a direct proof of their equivariant version of the Atiyah–Hirzebruch isomorphism.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/978-3-030-34953-0_5
