## Universal polynomials in lambda rings and the K-theory of the infinite loop space tmf

##### Author(s)

Hopkinson, John R. (John Robert)
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Michael J. Hopkins.

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Show full item record##### 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).

##### Date issued

2006##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.