93 citations · 133 across the 9 of their papers we have counts for
10 papers
Khovanov homology detects the figure-eight knot
John A. Baldwin, Nathan Dowlin, Adam Simon Levine +2
Using Dowlin's spectral sequence from Khovanov homology to knot Floer homology, we prove that reduced Khovanov homology (over ) detects the figure-eight knot.
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 spectral sequence from Khovanov homology to knot Floer homology
Nathan Dowlin
A well-known conjecture of Rasmussen states that for any knot in , the rank of the reduced Khovanov homology of is greater than or equal to the rank of the reduced k…
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…
A family of -like invariants in knot Floer homology
Nathan Dowlin
We define and study a family of link invariants . Although these homology theories are defined using holomorphic disc counts, they share many properties with $…
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…
A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homology
Nathan Dowlin
Let be the spectral sequence induced by the oriented cube of resolutions on knot Floer homology. We prove that is a triply graded link invariant whose…
Knot Floer Homology and Khovanov-Rozansky Homology for Singular Links
Nathan Dowlin
The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex to a singular resolution of a knot . Manolescu conjectured that when is…
The Knot Floer Cube of Resolutions and the Composition Product
Nathan Dowlin
We examine the relationship between the (untwisted) knot Floer cube of resolutions and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard di…
The Role of Mergers in Early-type Galaxy Evolution and Black Hole Growth
Kevin Schawinski, Nathan Dowlin, Daniel Thomas +2
Models of galaxy formation invoke the major merger of gas-rich progenitor galaxies as the trigger for significant phases of black hole growth and the associated feedback that suppr…