Resolution of smooth group actions
A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types i...
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| Format: | Article |
| Language: | en_US |
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American Mathematical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/82004 https://orcid.org/0000-0002-1494-8228 |
| _version_ | 1826205487156166656 |
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| author | Albin, Pierre Melrose, Richard B. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Albin, Pierre Melrose, Richard B. |
| author_sort | Albin, Pierre |
| collection | MIT |
| description | A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution structure’ consisting of equivariant iterated fibrations of the boundary faces. This structure projects to give a similar resolution structure for the quotient. In particular these results apply to give a canonical resolution of the radial compactification, to a ball, of any finite dimensional representation of a compact Lie group; such resolutions of the normal action of the isotropy groups appear in the boundary fibers in the general case. |
| first_indexed | 2024-09-23T13:13:53Z |
| format | Article |
| id | mit-1721.1/82004 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:13:53Z |
| publishDate | 2013 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/820042022-10-01T13:52:28Z Resolution of smooth group actions Albin, Pierre Melrose, Richard B. Massachusetts Institute of Technology. Department of Mathematics Melrose, Richard B. A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution structure’ consisting of equivariant iterated fibrations of the boundary faces. This structure projects to give a similar resolution structure for the quotient. In particular these results apply to give a canonical resolution of the radial compactification, to a ball, of any finite dimensional representation of a compact Lie group; such resolutions of the normal action of the isotropy groups appear in the boundary fibers in the general case. National Science Foundation (U.S.) (Graduate Research Fellowship) National Science Foundation (U.S.) (NSF grant DMS-0635607002) National Science Foundation (U.S.) (NSF grant DMS-1005944) 2013-11-06T19:36:02Z 2013-11-06T19:36:02Z 2010 Article http://purl.org/eprint/type/JournalArticle 978-0-8218-4948-4 http://hdl.handle.net/1721.1/82004 Albin, Pierre and Richard Melrose. "Resolution of smooth group actions." In p.1-26. Mazim Braverman, et al (Eds.), Spectral theory and geometric analysis: an international conference in honor of Mikhail Shubins's 65th birthday, July 29-August 2, 2009, Northeastern University, Boston, Massachusetts. (Contemporary mathematics; v. 535). https://orcid.org/0000-0002-1494-8228 en_US http://books.google.com/books?id=1sauAAGjBbcC&pg=PA1&lpg=PA1&dq=Resolution+of+Smooth+Group+Actions&source=bl&ots=Wq6YNPw43b&sig=6d2KB6K5XTw1xmfGP8_Acz_E65g&hl=en&sa=X&ei=ihUqUuuLE6uh4APV7oHACw&ved=0CDYQ6AEwAQ#v=onepage&q=Resolution%20of%20Smooth%20Group%20Actions&f=false Spectral theory and geometric analysis Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf American Mathematical Society arXiv |
| spellingShingle | Albin, Pierre Melrose, Richard B. Resolution of smooth group actions |
| title | Resolution of smooth group actions |
| title_full | Resolution of smooth group actions |
| title_fullStr | Resolution of smooth group actions |
| title_full_unstemmed | Resolution of smooth group actions |
| title_short | Resolution of smooth group actions |
| title_sort | resolution of smooth group actions |
| url | http://hdl.handle.net/1721.1/82004 https://orcid.org/0000-0002-1494-8228 |
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