Results on Algebraic Realization of Equivariant Bundles Over the 2-Sphere
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2016-08
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University of Hawaii at Manoa
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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.
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Algebraic topology, real algebraic sets, equivariant complex vector bundle, Lie group actions
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Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Math
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