Equivariant K-theory and Resolution I: Abelian Actions
© 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 fibr...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Book chapter |
| Language: | English |
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Springer International Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/137509 |
| _version_ | 1826189342140268544 |
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| author | Dimakis, P Melrose, R |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Dimakis, P Melrose, R |
| author_sort | Dimakis, P |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T08:13:14Z |
| format | Book chapter |
| id | mit-1721.1/137509 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:13:14Z |
| publishDate | 2021 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1375092023-02-09T16:27:38Z Equivariant K-theory and Resolution I: Abelian Actions Dimakis, P Melrose, R Massachusetts Institute of Technology. Department of Mathematics © 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. 2021-11-05T15:10:06Z 2021-11-05T15:10:06Z 2020 2021-05-24T17:49:57Z Book chapter http://purl.org/eprint/type/BookItem https://hdl.handle.net/1721.1/137509 Dimakis, P and Melrose, R. 2020. "Equivariant K-theory and Resolution I: Abelian Actions." 333. en 10.1007/978-3-030-34953-0_5 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer International Publishing arXiv |
| spellingShingle | Dimakis, P Melrose, R Equivariant K-theory and Resolution I: Abelian Actions |
| title | Equivariant K-theory and Resolution I: Abelian Actions |
| title_full | Equivariant K-theory and Resolution I: Abelian Actions |
| title_fullStr | Equivariant K-theory and Resolution I: Abelian Actions |
| title_full_unstemmed | Equivariant K-theory and Resolution I: Abelian Actions |
| title_short | Equivariant K-theory and Resolution I: Abelian Actions |
| title_sort | equivariant k theory and resolution i abelian actions |
| url | https://hdl.handle.net/1721.1/137509 |
| work_keys_str_mv | AT dimakisp equivariantktheoryandresolutioniabelianactions AT melroser equivariantktheoryandresolutioniabelianactions |