Completion of Dominant K-theory

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dc.contributor.advisorSpicer, James B.
dc.contributor.committeeMemberKitchloo, Nitu
dc.contributor.committeeMemberMorava, Jack J.
dc.contributor.committeeMemberWilson, W. Stephen
dc.contributor.committeeMemberMaksimovic, Petar
dc.creatorCattell, Stephen E.
dc.creator.orcid0000-0001-5970-9637
dc.date.accessioned2017-04-19T12:26:52Z
dc.date.available2017-04-19T12:26:52Z
dc.date.created2016-08
dc.date.issued2016-07-25
dc.date.submittedAugust 2016
dc.date.updated2017-04-19T12:26:52Z
dc.description.abstractNitu Kitchloo generalized equivariant K-theory to include non-compact Kac-Moody groups, calling the new theory Dominant K-theory. For a non-compact Kac-Moody group there are no non-trivial finite dimensional dominant representations, so there is no notion of a augmentation ideal, and the spaces we can work with have to have compact isotropy groups. To resolve these we complete locally, at the compact subgroups. We show that there is a 1 dimensional representation in the dominant representation ring such that when inverted we recover the regular representation ring. This shows that if H is a compact subgroup of a Kac-Moody group K(A), the completion of the Dominant K-theory of a H-space X is identical to the equivariant K-theory completed at the augmentation ideal. This is the local information. To glue this together we find a new spectrum whose cohomology theory is isomorphic to K ∗ (X × K EK). This enables us to use compute K ∗ (X × K EK) using a skeletal filtration as we now know the E 1 page of this spectral sequence is formed out of known algebras.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://jhir.library.jhu.edu/handle/1774.2/40345
dc.language.isoen_US
dc.publisherJohns Hopkins University
dc.publisher.countryUSA
dc.subjectK-theory
dc.subjectAlgebraic Topology
dc.titleCompletion of Dominant K-theory
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorJohns Hopkins University
thesis.degree.grantorKrieger School of Arts and Sciences
thesis.degree.levelDoctoral
thesis.degree.namePh.D.
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