Joshua Wang

collaborators

4 papers

math.GT2026

Link homology and loop homology

Joshua Wang

We compute the $k$ -colored $sl (N)$ homology of the torus knot $T (2, 2 m + 1)$ , and we show that it stabilizes as $m \to \infty$ to the integral homology of the free loop space…

math.GT2026

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…

math.GT2025

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…

math.GT2025

Stable deformed $gl_{N}$ homology of torus knots

William Ballinger, Eugene Gorsky, Matthew Hogancamp +1

We compute the $E_{2}$ page in the Rasmussen spectral sequence from triply graded to $gl_{N}$ Khovanov--Rozansky stable homology of torus knots. This confirms a weak form of…

Link homology and loop homology

The minimal Rickard complexes of braids on two strands

Colored sl(N) homology and SU(N) representations

Stable deformed glN​ homology of torus knots

Stable deformed $gl_{N}$ homology of torus knots