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Title: Fiber Bundles in Analytic, Zariski, and Etale Topologies
Authors: Murayama, Takumi
Advisors: Kollar, Janos
Contributors: Patakfalvi, Zsolt
Department: Mathematics
Class Year: 2014
Abstract: We compare the behavior of fiber bundles with structure group 𝐺 for 𝐺 the general linear group GL, the projective general linear group PGL, and the general affine group GA. We prove a criterion for when a GA-bundle is in fact a GL-bundle, i.e., a vector bundle, over the Riemann sphere ℙ1. We also discuss the behavior of fiber bundles under different topologies; specifically, we compare the analytic versus Zariski topologies over the Riemann sphere ℙ1,and compare the étale and Zariski topologies on schemes in general.
Extent: 36 pages
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2020

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