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Results on Algebraic Realization of Equivariant Bundles Over the 2-Sphere

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Item Summary

Title:Results on Algebraic Realization of Equivariant Bundles Over the 2-Sphere
Authors:Verrette, Jean
Keywords:algebraic topology
real algebraic sets
equivariant complex vector bundle
Lie group actions
Date Issued:Aug 2016
Publisher:[Honolulu] : [University of Hawaii at Manoa], [August 2016]
Abstract:We verify the Algebraic Realization Conjecture for complex equivariant vector bundles over the 2-sphere with effective actions by the rotational symmetries of the tetrahedron, octahedron, and icosahedron. We introduce three strongly algebraic complex line bundles over the 2-sphere by direct construction of classifying maps. We demonstrate how every equivariant complex line bundle is a tensor product of these three established strongly algebraic bundles, and any equivariant complex vector bundle over the 2-sphere is a Whitney sum of equivariant complex line bundles. Our classification proofs rely on equivariant CW complex constructions and the induced equivariant pointed cofibration sequences.
Description:Ph.D. University of Hawaii at Manoa 2016.
Includes bibliographical references.
Appears in Collections: Ph.D. - Mathematics

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