8 citations · 16 across the 11 of their papers we have counts for
11 papers · 1 filter
Link homology and loop homology
Joshua Wang
We compute the -colored homology of the torus knot , and we show that it stabilizes as to the integral homology of the free loop space…
The minimal Rickard complexes of braids on two strands
Joshua Wang
The Rickard complex of a braid with strands colored by positive integers is a chain complex of singular Soergel bimodules. The complex determines the colored triply-graded homology…
Stable deformed homology of torus knots
William Ballinger, Eugene Gorsky, Matthew Hogancamp +1
We compute the page in the Rasmussen spectral sequence from triply graded to Khovanov--Rozansky stable homology of torus knots. This confirms a weak form of…
A minimality property for knots without Khovanov 2-torsion
Onkar Singh Gujral, Joshua Wang
A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology. We show that if a knot has no 2-torsion in its Khovanov homology, then th…
The Gysin sequence and the sl(N) homology of T(2,m)
Joshua Wang
The sl(N) homology of the torus knot or link T(2,m) may be calculated explicitly. By direct comparison, the result is isomorphic to the cohomology of a naturally associated space o…
Colored sl(N) homology and SU(N) representations
Joshua Wang
We provide the first complete computations of colored sl(N) homology for a nontrivial knot. In doing so, we show that the colored sl(N) homology of the trefoil labeled by an exteri…
On sl(N) link homology with mod N coefficients
Joshua Wang
We construct an operator on sl(N) link homology with coefficients in a ring whose characteristic divides N. When P is prime, we use this operator to exhibit structural features of…
Split link detection for sl(P) link homology in characteristic P
Joshua Wang
If is a prime number, we show that reduced link homology with coefficients in detects split links. The argument uses Dowlin's spectral sequenc…
Link Floer homology also detects split links
Joshua Wang
Inspired by work of Lipshitz-Sarkar, we show that the module structure on link Floer homology detects split links. Using results of Ni, Alishahi-Lipshitz, and Lipshitz-Sarkar, we e…
The cosmetic crossing conjecture for split links
Joshua Wang
Given a band sum of a split two-component link along a nontrivial band, we obtain a family of knots indexed by the integers by adding any number of full twists to the band. We show…
A combinatorial proof of invariance of double-point enhanced grid homology
Timothy Ratigan, Joshua Wang, Luya Wang
We prove that the "minus" version of Lipshitz's double-point enhanced grid homology is a knot invariant through purely combinatorial means.