Universal polynomials in lambda rings and the K-theory of the infinite loop space tmf
Author(s)Hopkinson, John R. (John Robert)
Massachusetts Institute of Technology. Dept. of Mathematics.
Michael J. Hopkins.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 100-101).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology