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Morse-Bott Spectral Sequences and the Links of Singularities : 모스-보트 스펙트럴 수열과 특이점의 고리
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- Authors
- Advisor
- Otto van Koert
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2017-02
- Publisher
- 서울대학교 대학원
- Keywords
- Morse-Bott spectral sequence ; link of singularity ; symplectic homology ; Milnor fiber ; mean Euler characteristic
- Description
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2017. 2. Otto van Koert.
- Abstract
- In this thesis, we construct spectral sequences converging to symplectic homology and equivariant symplectic homology groups. We use Morse-Bott type Hamiltonians and a natural action filtration. Those spectral sequences are called Morse-Bott spectral sequences. We apply the spectral sequences to a certain kind of symplectic manifolds with boundary, namely Milnor fibers whose boundaries are the links of singularities. In special cases, such as links of weighted homogeneous polynomials, they admit a nice symmetry along a periodic Reeb flow of a contact form. By means of those special symmetric feature, we present a systematic way of computing equivariant symplectic homology groups and its mean Euler characteristic. We obtain several applications of these machineries to exotic contact structures.
- Language
- English
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