Xiao Wang

collaborators

3 papers

math.GT2026

Kauffman bracket skein homology from Heegaard splittings

Yin Tian, Xiao Wang

We extend the Kauffman bracket skein module of three manifolds to a homology theory in a combinatorial way. The resulting homology depends on Heegaard splittings of three manifolds…

math.QA2025

Homology of Yang-Baxter modules

Yin Tian, Xiao Wang, Yuxin Zhang

We study the Yang-Baxter operator for the vector representation $V_{m}$ of the quantum group $U_{q} (s l_{m})$ . We consider the one-term Yang-Baxter homology with coefficients in $V_{m}$ -mod…

math.GT2025

Low Dimensional Homology of the Yang-Baxter Operators Yielding the HOMFLYPT Polynomial

Anthony Christiana, Ben Clingenpeel, Huizheng Guo +4

In this paper, we analyze the homology of the Yang-Baxter Operators $R_{(m)}$ yielding the HOMFLYPT polynomial, reducing the computation of the $n$ -th homology of $R_{(m)}$ for arb…