2 citations · 3 across the 7 of their papers we have counts for
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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…
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…
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…