Related papers: Peculiar modules for 4-ended tangles
We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin$^c$ structures, generalising the correction terms (or $d$--invariants) defined by Ozsv\'ath and…
A previous result about the decategorified bordered (sutured) Heegaard Floer invariants of surfaces glued together along intervals, generalizing the decategorified content of Rouquier and the author's higher-tensor-product-based gluing…
In joint work with J. Rasmussen, we gave an interpretation of Heegaard Floer homology for manifolds with torus boundary in terms of immersed curves in a punctured torus. In particular, knot Floer homology is captured by this invariant.…
We give a precise description of splicing formulas from a previous paper in terms of knot Floer complex associated with a knot in homology sphere.
We describe a simple formula for computing the Heegaard Floer multicurve invariant of double tangles from the Heegaard Floer multicurve invariant of knot complements. A comparison with a similar multicurve invariant for Conway tangles in…
We use invariants of Hendricks and Manolescu coming from involutive Heegaard Floer theory to find constraints on possible configurations of singular points of a rational cuspidal curve of odd degree in the projective plane. We show that the…
Let K \subset Y be a knot in a three manifold which admits a longitude-framed surgery such that the surgered manifold has first Betti number greater than that of Y. We find a formula which computes the twisted Floer homology of the surgered…
We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the…
We prove a conjecture of Migdail and Wehrli regarding the odd Khovanov cobordism maps associated to knotted spheres. Our key tool is Daemi's plane Floer homology, which we use in place of a Lee deformation. Continuing the analogy with Lee…
We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to…
We review the construction of Heegaard Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link…
For 3-manifolds with torus boundary, the bordered Heegaard Floer invariants of Lipshitz--Ozsv\'ath--Thurston have a geometric interpretation as immersed multi-curves with local systems in the punctured torus according to the work of…
Starting from a Heegaard splitting of a three-manifold, we use Lagrangian Floer homology to construct a three-manifold invariant, in the form of a relatively Z/8-graded abelian group. Our motivation is to have a well-defined symplectic side…
We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a…
We prove that, up to local equivalences, a suitable truncation of the involutive knot Floer homology of a knot in $S^3$ and the involutive bordered Heegaard Floer theory of its complement determine each other. In particular, given two knots…
We extend Perutz's Lagrangian matching invariants to 3-manifolds which are not necessarily fibred using the technology of holomorphic quilts. We prove an isomorphism of these invariants with Ozsvath-Szabo's Heegaard Floer invariants for…
We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a 2-component link $L$ in $S^3$. We then specialise this…
We construct a variant of Floer homology groups and prove a gluing formula for a variant of Donaldson invariants. As a corollary, the variant of Donaldson invariants is non-trivial for connected sums of 4-manifolds which satisfy a condition…
We prove that the Lipshitz-Ozsv\'ath-Thurston correspondence between extended type D structures of knot complements and $\mathbb{F}[U, V]/(UV)$ knot Floer complexes can be arranged so that $\iota_K$-invariant splittings of knot Floer chain…
Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented 4-dimensional cobordisms. Bordered Heegaard Floer homology…