相关论文: Trisections and Ozsvath-Szabo cobordism invariants
We show that a quasipositive surface with disconnected boundary induces a map between the knot Floer homology groups of its boundary components preserving the transverse invariant. As an application, we show that this invariant can be used…
We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CF_r. It carries information about the Floer homology…
Meier and Zupan showed that every surface in the four-sphere admits a bridge trisection and can therefore be represented by three simple tangles. This raises the possibility of applying methods from link homology to knotted surfaces. We use…
We use Floer's exact triangle to study the u-map (cup product with the 4-dimensional class) in the Floer cohomology groups of admissible SO(3) bundles over closed, oriented 3-manifolds. In the case of non-trivial bundles we show that…
We give formulae for the Ozsvath-Szabo invariants of 4-manifolds X obtained by fiber sum of two manifolds M_1, M_2 along surfaces S_1, S_2 having trivial normal bundle and genus g>0. The formulae follow from a general theorem on the…
We outline the proof that non-triangulable manifolds exist in any dimension greater than four. The arguments involve homology cobordism invariants coming from the Pin(2) symmetry of the Seiberg-Witten equations. We also explore a related…
In this paper, we give an algorithm to compute the hat version of the Heegaard Floer homology of a closed oriented three-manifold. This method also allows us to compute the filtrations coming from a null-homologous link in a three-manifold.
Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded…
We use involutive Heegaard Floer homology to extend the Ozsv\'ath-Szab\'o branched double cover spectral sequence relating a version of Khovanov homology and the Heegaard Floer homology of branched double covers. Our main tools are…
We construct a product on the Floer complex associated to a pair of Lagrangian cobordisms. More precisely, given three exact transverse Lagrangian cobordisms in the symplectization of a contact manifold, we define a map $\mathfrak{m}_2$ by…
We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres.…
In this note we classify the diffeomorphism classes rel. boundary of smooth h-cobordisms between two fixed 1-connected 4-manifolds in terms of isometries between the intersection forms.
Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a…
We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of…
In these notes, we describe several geometric interpretations of $H^2(X)$ when $X$ is a trisected 4-manifold. The main insight is that, by analogy with Hodge theory and sheaf cohomology in algebraic geometry, classes in $H^2(X)$ can be…
We explore the Fourier transform of the Heegaard Floer $d$-invariants, which is particularly well-behaved with respect to connected sum. As corollaries, we show that lens spaces are cancellable in the monoid of 3-manifolds up to integer…
Fintushel and Stern have proved that if S \subset X is a symplectic surface in a symplectic 4-manifold such that S has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent…
We define a notion of Heegaard Floer homology for three dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected.
A generic smooth map of a closed $2k$-manifold into $(3k-1)$-space has a finite number of cusps ($\Sigma^{1,1}$-singularities). We determine the possible numbers of cusps of such maps. A fold map is a map with singular set consisting of…
We prove that there are homology three-spheres that bound definite four-manifolds, but any such bounding four-manifold must be built out of many handles. The argument uses the homology cobordism invariant $\Gamma$ from instanton Floer…