1 citations · 1 across the 2 of their papers we have counts for
5 papers
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…
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…