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Seiberg—Witten—Floer Homology and Gluing Formulae
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作者 AlanL.CAREY BaiLingWANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第2期245-296,共52页
This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an em... This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained. 展开更多
关键词 3 MANIFOLDS Seiberg WITTEN floer homology Seiberg Witten invariants Gluing formulae
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On the Equivalence of Multiplicative Structures in Floer Homology and Quantum Homology
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作者 Gang LiuDepartment of Mathematics,UCLA,Los Angeles,CA 90095 USAGang TianDepartment of Mathematics,MIT,Cambridge,MA 02139,USA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1999年第1期53-80,共28页
In this paper,we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring.We will also prove that GW-invariants in Floer homology and quantum ho... In this paper,we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring.We will also prove that GW-invariants in Floer homology and quantum homology are equivalent. 展开更多
关键词 floer homology Quantum homology GW-invariants J-holomorphic curves Moduli space
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The Symplectic Floer Homology of the Square Knot and Granny Knots
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作者 Weiping LiDepartment of Mathematics,Oklahoma State University,Stillwater,Oklahoma 74078-0613,USA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1999年第1期1-10,共10页
Using a kind of Mayer-Vietoris principle for the symplectic Floer homology of knots,we compute the symplectic Floer homology of the square knot and granny knots.
关键词 KNOT Knot Cobordism Maslov Index floer homology
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A Note on Knot Floer Homology and Fixed Points of Monodromy
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作者 Yi Ni 《Peking Mathematical Journal》 CSCD 2023年第2期635-643,共9页
Using an argument of Baldwin-Hu-Sivek,we prove that if K is a hyperbolic fibered knot with fiber F in a closed,oriented 3-manifold Y,andHFK(Y,K,[F],g(F)−1)has rank 1,then the monodromy of K is freely isotopic to a pse... Using an argument of Baldwin-Hu-Sivek,we prove that if K is a hyperbolic fibered knot with fiber F in a closed,oriented 3-manifold Y,andHFK(Y,K,[F],g(F)−1)has rank 1,then the monodromy of K is freely isotopic to a pseudo-Anosov map with no fixed points.In particular,this shows that the monodromy of a hyperbolic L-space knot is freely isotopic to a map with no fixed points. 展开更多
关键词 Knot floer homology Fibered knot Fixed points L-space knot
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