Smooth K-theory and locally convex algebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/29357 |
| _version_ | 1811072703073878016 |
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| author | Lakos, Gyula, 1973- |
| author2 | Richard B. Melrose. |
| author_facet | Richard B. Melrose. Lakos, Gyula, 1973- |
| author_sort | Lakos, Gyula, 1973- |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. |
| first_indexed | 2024-09-23T09:10:31Z |
| format | Thesis |
| id | mit-1721.1/29357 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T09:10:31Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/293572019-04-10T21:10:48Z Smooth K-theory and locally convex algebras Lakos, Gyula, 1973- Richard B. Melrose. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. Includes bibliographical references (p. 121-122). In this thesis, we improve the loop linearization process from the classical article of Atiyah and Bott on Bott periodicity. The linearization process is made explicit in terms of formulae for smooth loops. Using this improvement allows us to extend K-theory (including periodicity) to a class of locally convex algebras vastly larger then the one of Banach algebras. We find various ways to represent periodicity by explicit formulae. For finite Laurent loops formulae yielding finite matrices to represent the associated Ko classes are obtained. The methods used also allow us to reinterpret some recent results of Melrose on smooth classifying spaces for K-theory. The relationship between the universal even and odd Chern characters and periodicity is investigated, giving correspondences between the various representatives in the form of family index theorems for loop groups. In the discussion Ko and the even Chern character are primarily formulated in the language of involutions. The paper also demonstrates the universality of the involution terminology with respect to vector bundles. by Gyula Lakos. Ph.D. 2005-10-14T20:03:20Z 2005-10-14T20:03:20Z 2003 2003 Thesis http://hdl.handle.net/1721.1/29357 52769648 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 122 p. 3618935 bytes 3618744 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Lakos, Gyula, 1973- Smooth K-theory and locally convex algebras |
| title | Smooth K-theory and locally convex algebras |
| title_full | Smooth K-theory and locally convex algebras |
| title_fullStr | Smooth K-theory and locally convex algebras |
| title_full_unstemmed | Smooth K-theory and locally convex algebras |
| title_short | Smooth K-theory and locally convex algebras |
| title_sort | smooth k theory and locally convex algebras |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/29357 |
| work_keys_str_mv | AT lakosgyula1973 smoothktheoryandlocallyconvexalgebras |