Universal polynomials in lambda rings and the K-theory of the infinite loop space tmf
Name
71011847-MIT.pdf
Description
Full printable version
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6.44 MB
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Checksum (MD5)
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Author(s)
Hopkinson, John R. (John Robert)
Advisor(s)
Michael J. Hopkins.
Date Issued
2006
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
Includes bibliographical references (p. 100-101).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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