Snaith, Victor P. (1969) Some topics in K-theory. PhD thesis, University of Warwick.

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Abstract

In part A (II) the uniqueness theorem for equivariant cohomology theories, (proved in part A (I)), is used to calculate the operation rings, Op(KG,KG^) and OP(KG^,KG^), (^ is I(G)-adic completion ; G is a finite group). Semi-groups, SG < KG, are introduced and Op(~SG(-), KG) is calculated in order to investigate (Op(KG), the ring of self-operations of KG. Finally Op(KG) is related to the other two rings of operations and any self-operation of KG is proved to be continuous with respect to the I(G)-adic topology.

In Part B some higher order operations in K-theory, called Massey products, are defined and proved to be the differentials in the Equivariant Kunneth Formula spectral sequence in K-theory.

In Part C the Rothenberg-Steenrod spectral sequences are used (i) to calculate the K-theory of conjugate bundles of Lie groups, (ii) to prove a small theorem on the K-theory of homogeneous spaces of Lie groups, and (iii) to calculate the homological dimension of R(H) as an R(G)-module, for an inclusion of Lie groups, H<G. As an example of (ii) the algebra K (SO(m)) and the operation ring, lim<--- K(SO(m)), are computed.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	K-theory
Official Date:	1969
Dates:	Date Event 1969 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hodgkin, Luke Howard, 1938-
Extent:	57, [3], 34, 35 leaves.
Language:	eng

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