2026-09-20T03:07:54Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/345442022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Michael J. Hopkins.
Hopkinson, John R. (John Robert)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-11-07T12:53:04Z
2006-11-07T12:53:04Z
2006
2006
http://hdl.handle.net/1721.1/34544
71011847
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
Includes bibliographical references (p. 100-101).
The algebraic structure of the K-theory of a topological space is described by the more general notion of a lambda ring. We show how computations in a lambda ring are facilitated by the use of Adams operations, which are ring homomorphisms, and apply this principle to understand the algebraic structure. In a torsion free ring the Adams operations completely determine the lambda ring. This principle can be used to determine the K-theory of an infinite loop space functorially in terms of the K-theory of the corresponding spectrum. In particular we obtain a description of the K-theory of the infinite loop space tmf in terms of Katz's ring of divided congruences of modular forms. At primes greater than 3 we can also relate this to a Hecke algebra.
by John R. Hopkinson.
Ph.D.
101 p.
6748159 bytes
6752339 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Universal polynomials in lambda rings and the K-theory of the infinite loop space tmf
Thesis
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