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
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
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
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.
基金The author was partially supported by NSF Grant Number DMS-1811900.
文摘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.
文摘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.
文摘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.
文摘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.
