21 citations · 59 across the 15 of their papers we have counts for
16 papers
Colored knot Floer homology: structures and examples
Akram Alishahi, Eugene Gorsky, Beibei Liu
Inspired by the colored version of Khovanov and Khovanov-Rozansky homology, we define a colored version of knot Floer homology by studying the colimit of a directed system of…
Detecting Heegaard Floer homology solid tori
Akram Alishahi, Tye Lidman, Robert Lipshitz
We show that a rational homology solid torus is a Heegaard Floer homology solid torus if and only if it has a Dehn filling with a non-separating 2-sphere. Using this, we characteri…
Bordered Floer homology, handlebody detection, and compressing diffeomorphisms
Akram Alishahi, Robert Lipshitz
We show that, up to connected sums with integer homology -spaces, bordered Floer homology detects handlebodies, as well as whether a mapping class extends over a given handlebod…
Splitting maps in link Floer homology and integer points in permutahedra
Akram Alishahi, Eugene Gorsky, Beibei Liu
In this paper, we study the skein exact sequence for links via the exact surgery triangle of link Floer homology and compare it with other skein exact sequences given by Ozsváth an…
Khovanov homology and the Involutive Heegaard Floer homology of branched double covers
Akram Alishahi, Linh Truong, Melissa Zhang
We use involutive Heegaard Floer homology to extend the Ozsváth-Szabó branched double cover spectral sequence relating a version of Khovanov homology and the Heegaard Floer homolog…
Upsilon invariant for graphs and the homology cobordism group of homology cylinders
Akram Alishahi
Upsilon is a homomorphism on the smooth concordance group of knots defined by Ozsváth, Stipsicz and Szabó. In this paper, we define a generalization of upsilon for a family of embe…
A friendly introduction to the bordered contact invariant
Akram Alishahi, Joan Licata, Ina Petkova +1
We give a short introduction to the contact invariant in bordered Floer homology defined by Földvári, Hendricks, and the authors. The construction relies on a special class of foli…
Bordered Floer homology and contact structures
Akram Alishahi, Viktória Földvári, Kristen Hendricks +3
We introduce a contact invariant in the bordered sutured Heegaard Floer homology of a three-manifold with boundary. The input for the invariant is a contact manifold $(M, ξ, \mathc…
Relating tangle invariants for Khovanov homology and knot Floer homology
Akram Alishahi, Nathan Dowlin
Ozsvath and Szabo recently constructed an algebraically defined invariant of tangles which takes the form of a DA bimodule. This invariant is expected to compute knot Floer homolog…
A link invariant related to Khovanov homology and knot Floer homology
Akram Alishahi, Nathan Dowlin
In this paper we introduce a chain complex where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction i…
Knot Floer homology and the unknotting number
Akram Alishahi, Eaman Eftekhary
Given a knot K in S^3, let u^-(K) (respectively, u^+(K)) denote the minimum number of negative (respectively, positive) crossing changes among all unknotting sequences for K. We us…
The Lee Spectral Sequence, Unknotting Number, and the Knight Move Conjecture
Akram Alishahi, Nathan Dowlin
We show that the page at which the Lee spectral sequence collapses gives a bound on the unknotting number, u(K). In particular, for knots with u(K)<3, we show that the Lee spectral…
The Bar-Natan homology and unknotting number
Akram Alishahi
We show that the order of torsion homology classes in Bar-Natan deformation of Khovanov homology is a lower bound for the unknotting number. We give examples of knots that this is…
Bordered Floer homology and incompressible surfaces
Akram Alishahi, Robert Lipshitz
We show that bordered Heegaard Floer homology detects incompressible surfaces and bordered-sutured Floer homology detects partly boundary parallel tangles and bridges, in natural w…
Tangle Floer homology and cobordisms between tangles
Akram Alishahi, Eaman Eftekhary
We introduce a generalization of oriented tangles, which are still called tangles, so that they are in one-to-one correspondence with the sutured manifolds. We define cobordisms be…
A refinement of sutured Floer homology
Akram S. Alishahi, Eaman Eftekhary
We introduce a refinement of the Ozsvath-Szabo complex associated to a balanced sutured manifold by Juhasz. An algebra is associated to the boundary of a sutured mani…