Related papers: Notes on bordered Floer homology
We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology…
In this paper we show how to recover the relative Q-grading in Heegaard Floer homology from the noncommutative grading on bordered Floer homology.
We use bordered Heegaard Floer homology to compute the tau invariant of a family of satellite knots obtained via twisted infection along two components of the Borromean rings, a generalization of Whitehead doubling. We show that tau of the…
We obtain a formula for the Heegaard Floer homology (hat theory) of the three-manifold $Y(K_1,K_2)$ obtained by splicing the complements of the knots $K_i\subset Y_i$, $i=1,2$, in terms of the knot Floer homology of $K_1$ and $K_2$. We also…
In this paper we find a family of knots with trivial Alexander polynomial, and construct two non-isotopic Seifert surfaces for each member in our family. In order to distinguish the surfaces we study the sutured Floer homology invariants of…
We prove a basic inequality for the d-invariants of a splice of knots in homology spheres. As a result, we are able to prove a new relation on the rank of reduced Floer homology under maps between Seifert fibered homology spheres, improving…
We prove the equivalence of the sutured versions of Heegaard Floer homology, monopole Floer homology, and embedded contact homology. As applications we show that the knot versions of Heegaard Floer homology and embedded contact homology are…
In this paper we extend the results of \cite{Plumbing} to calculate Ozsv\'ath-Szab\'o Floer homology group HF+ for a class of negative-semidefinite plumbings with b_1 = 1.
We calculate the Heegaard Floer homologies$HF^+(M,s) for mapping tori M associated to certain surface diffeomorphisms, where s is any Spin^c structure on M whose first Chern class is non-torsion. Let gamma and delta be a pair of…
The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in two earlier papers (math.SG/0101206 and math.SG/0105202). This four-dimensional theory also…
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 show that the graph TQFT for Heegaard Floer homology satisfies a strong version of Atiyah's duality axiom for a TQFT. As an application, we compute some Heegaard Floer mixed invariants of 4-dimensional mapping tori in terms of Lefschetz…
Given a double cover between 3-manifolds branched along a nullhomologous link, we establish an inequality between the dimensions of their Heegaard Floer homologies. We discuss the relationship with the L-space conjecture and give some other…
We review the use of grid diagrams in the development of Heegaard Floer theory. We describe the construction of the combinatorial link Floer complex, and the resulting algorithm for unknot detection. We also explain how grid diagrams can be…
We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk open book decomposition for (S^3,\xi_std), we associate a corresponding multi-pointed nice…
This is the author's PhD thesis, as submitted to the Princeton University. The results of this paper have already appeared in arXiv:math/0607777v4, arXiv:math/0607691 and arXiv:0901.2156.
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 show that the sutured Floer homology of a sutured 3-manifold of the form $(D^2 \times S^1, F \times S^1)$ can be expressed as the homology of a string-type complex, generated by certain sets of curves on $(D^2, F)$ and with a…
We make use of the action of $H_1(Y)$ in Heegaard Floer homology to generalize the Ozsv\'ath-Szab\'o correction terms for $3$-manifolds with standard $\operatorname{HF}^\infty$. We establish the basic properties of these invariants:…
We present two SageMath programs that build on and improve upon Sucharit Sarkar's hf-hat. Given an abstract open book and a collection of pairwise disjoint properly embedded arcs on a page of the open book, the first program, hf-hat-obd,…