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

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Official URL: http://webcat.warwick.ac.uk/record=b1732899~S1
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). Semigroups, SG < KG, are introduced and Op(~SG(), KG) is calculated in order to investigate (Op(KG), the ring of selfoperations of KG. Finally Op(KG) is related to the other two rings of operations and any selfoperation of KG is proved to be continuous with respect to the I(G)adic topology.
In Part B some higher order operations in Ktheory, called Massey products, are defined and proved to be the differentials in the Equivariant Kunneth Formula spectral sequence in Ktheory.
In Part C the RothenbergSteenrod spectral sequences are used (i) to calculate the Ktheory of conjugate bundles of Lie groups, (ii) to prove a small theorem on the Ktheory 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 or Dissertation (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Ktheory  
Official Date:  1969  
Dates: 


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Publication Status:  Unpublished  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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