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

dc.contributor.author	Verrette, Jean
dc.date.accessioned	2017-12-18T22:12:45Z
dc.date.available	2017-12-18T22:12:45Z
dc.date.issued	2016-08
dc.description.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.
dc.description.degree	Ph.D.
dc.identifier.uri	http://hdl.handle.net/10125/51514
dc.language	eng
dc.publisher	University of Hawaii at Manoa
dc.relation	Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Math
dc.subject	Algebraic topology
dc.subject	real algebraic sets
dc.subject	equivariant complex vector bundle
dc.subject	Lie group actions
dc.title	Results on Algebraic Realization of Equivariant Bundles Over the 2-Sphere
dc.type	Thesis
dc.type.dcmi	Text

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