2026-09-18T21:56:42Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/293572022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Richard B. Melrose.
Lakos, Gyula, 1973-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-10-14T20:03:20Z
2005-10-14T20:03:20Z
2003
2003
http://hdl.handle.net/1721.1/29357
52769648
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.
122 p.
3618935 bytes
3618744 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Smooth K-theory and locally convex algebras
Thesis
application/pdf
Publication
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