Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Dowlin, Nathan"'
Using Dowlin's spectral sequence from Khovanov homology to knot Floer homology, we prove that reduced Khovanov homology (over $\mathbb{Q}$) detects the figure-eight knot.
Externí odkaz:
http://arxiv.org/abs/2007.01269
Autor:
Alishahi, Akram, Dowlin, Nathan
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 homology. The authors have a similar construction for open braids and their p
Externí odkaz:
http://arxiv.org/abs/1909.03865
Autor:
Dowlin, Nathan
A well-known conjecture of Rasmussen states that for any knot $K$ in $S^{3}$, the rank of the reduced Khovanov homology of $K$ is greater than or equal to the rank of the reduced knot Floer homology of $K$. This rank inequality is supposed to arise a
Externí odkaz:
http://arxiv.org/abs/1811.07848
Autor:
Alishahi, Akram, Dowlin, Nathan
In this paper we introduce a chain complex $C_{1 \pm 1}(D)$ where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction is purely algebraic. It is constructed as an oriented cube of resolutio
Externí odkaz:
http://arxiv.org/abs/1810.13406
Autor:
Dowlin, Nathan
We define and study a family of link invariants $\mathit{HFK}_{n}(L)$. Although these homology theories are defined using holomorphic disc counts, they share many properties with $sl_{n}$ homology. Using these theories, we give a framework that gener
Externí odkaz:
http://arxiv.org/abs/1804.03165
Autor:
Alishahi, Akram, Dowlin, Nathan
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 sequence must collapse at the E_2 page. An immediate corollary is tha
Externí odkaz:
http://arxiv.org/abs/1710.07875
Autor:
Dowlin, Nathan
Let $E_{k}^{F}(D)$ be the spectral sequence induced by the oriented cube of resolutions on knot Floer homology. We prove that $E_{2}^{F}(D)$ is a triply graded link invariant whose graded Euler characteristic is the HOMFLY-PT polynomial and that the
Externí odkaz:
http://arxiv.org/abs/1703.01401
Autor:
Dowlin, Nathan
Publikováno v:
Algebr. Geom. Topol. 18 (2018) 3839-3885
The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex $C_{F}(S)$ to a singular resolution $S$ of a knot $K$. Manolescu conjectured that when $S$ is in braid position, the homology $H_{*}(C_{F}(S))$ is isomorphic to th
Externí odkaz:
http://arxiv.org/abs/1511.08953
Autor:
Dowlin, Nathan
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 diagram for a knot $K$, we see that the filtered complex decomposes as a
Externí odkaz:
http://arxiv.org/abs/1508.03037
Autor:
Dowlin, Nathan
Publikováno v:
Journal of the American Mathematical Society; 2024, Vol. 37 Issue 4, p951-1010, 60p
