(The) infinite family of symplectic tori in a fixed homology class고정된 호몰로지 클래스에서의 심플렉틱 토러스들의 무한군

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Ronald Fintushel and Ronald J. Stern have proved the following theorem : \begin{thm} Let $X$ be a simply connected symplectic 4-manifold which contains a c-embedded symplectic torus $T$. Then in each homology class $2m[T]$, $m\geq 2$, there is an infinite family of smoothly embedded symplectic tori, no two of which are smoothly isotopic. \end{thm} To say that a torus $T$ is $c-embedded$ means that $T$ is a smoothly embedded homologically essential torus of self-intersection zero which has a pair of simple curves which generate its first homology and which bound vanishing cycles (disks of self-intersection $-1$) in $X$. We will prove this theorem with different model from Birman and Menasco which R. Fintushel and R. J. Stern have used. We shall make proof of it by showing that if two smoothly embedded symplectic tori are smoothly isotopic then their Alexander polynomials are equal and finding an infinite family of braids whose Alexander polynomials are all distinct.
Advisors
Suh, Dong-Youpresearcher서동엽researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2001
Identifier
166318/325007 / 000993282
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수학전공, 2001.2, [ 17 p. ]

Keywords

Seiberg-Witten invariant; symplectic; braid; 브레이드; 사이버그-위튼 불변수; 심플렉틱

URI
http://hdl.handle.net/10203/42031
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=166318&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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