Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01p2676v739
 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 URI: http://arks.princeton.edu/ark:/88435/dsp01p2676v739 Type of Material: Princeton University Senior Theses Language: en_US Appears in Collections: Mathematics, 1934-2016

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