Ian Sullivan

activity

20242026

collaborators

4 papers

math.GT2026

Handle decompositions and the 1-dimensional inputs skein lasagna module

Imogen Montague, Ian A. Sullivan

We establish handle attachment formulas for the Khovanov skein lasagna module with 1-dimensional inputs over $Q$ , defined recently by Ren, Wedrich, Willis, Zhang, and the…

math.GT2025

Khovanov skein lasagna modules with $1$ -dimensional inputs

Qiuyu Ren, Ian Sullivan, Paul Wedrich +2

We construct a variant of Khovanov skein lasagna modules, which takes the Khovanov homology in connected sums of $S^{1} \times S^{2}$ defined by Rozansky and Willis as the input link ho…

math.GT2025

Bar-Natan skein lasagna modules and exotic surfaces in 4-manifolds

Ian A. Sullivan

We construct and study the skein lasagna module obtained by importing the Bar-Natan Khovanov homology package. For 4-manifolds satisfying a non-vanishing condition, we produce pair…

math.GT2024

Kirby belts, categorified projectors, and the skein lasagna module of $S^{2} \times S^{2}$

Ian A. Sullivan, Melissa Zhang

We interpret Manolescu-Neithalath's cabled Khovanov homology formula for computing Morrison-Walker-Wedrich's $KhR_{2}$ skein lasagna module as a homotopy colimit (mapping te…

Handle decompositions and the 1-dimensional inputs skein lasagna module

Khovanov skein lasagna modules with 1-dimensional inputs

Bar-Natan skein lasagna modules and exotic surfaces in 4-manifolds

Kirby belts, categorified projectors, and the skein lasagna module of S2×S2

Khovanov skein lasagna modules with $1$ -dimensional inputs

Kirby belts, categorified projectors, and the skein lasagna module of $S^{2} \times S^{2}$