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Higher rank vector bundles in Fukaya category
푸카야 범주의 고차 벡터 다발

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Authors
배한울
Advisor
조철현
Major
자연과학대학 수리과학부
Issue Date
2017-08
Publisher
서울대학교 대학원
Keywords
라그랑지안 플로어 이론푸카야 범주평탄한 벡터 다발뒤틀린 복합체
Description
학위논문 (박사)-- 서울대학교 대학원 자연과학대학 수리과학부, 2017. 8. 조철현.
Abstract
In this thesis, we study higher rank vector bundles in Fukaya category and its relation with twisted complex. We enlarge the class of objects of Fukaya category so that they contain not only flat line bundles, but also any finite rank flat vector bundles. For this purpose we use the de Rham version of Fukaya category and verify that it has some nice features, which other versions do not share.

We prove that every flat vector bundle on a Lagrangian submanifold can be realized as a twisted complex of flat line bundles when the fundamental group of the Lagrangian submanifold is abelian. Futhermore, we also prove that every flat vector bundle whose holonomy reprsentation is triangularizable is quasi-isomorphic to a certain twisted complex of flat line bundles.
Language
English
URI
https://hdl.handle.net/10371/137160
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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