Yin Tian

collaborators

5 papers

math.SG2026

Higher-dimensional Heegaard Floer homology and spectral networks

Ko Honda, Yin Tian, Tianyu Yuan

Given a closed surface $C$ and a real exact Lagrangian $I^£ \subset T^{*} C$ associated to a spectral curve, we construct a homomorphism $\operatorname{BSk}_Îº(C)\to\operatorname{Mat}(N…

math.SG2025

Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras

Yuan Gao, Eilon Reisin-Tzur, Yin Tian +1

We show that the higher-dimensional Heegaard Floer homology between tuples of cotangent fibers and the conormal bundle of a homotopically nontrivial simple closed curve on $T^{2}$ re…

math.SG2025

Towards a symplectic Khovanov homology for links in fibered $3$ -manifolds

Vincent Colin, Ko Honda, Yin Tian

The goal of this paper is twofold: (i) define a symplectic Khovanov type homology for a transverse link in a fibered closed $3$ -manifold $M$ (with an auxiliary choice of a homotopy…

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.SG2025

Morse theory of loop spaces and Hecke algebras

Ko Honda, Roman Krutowski, Yin Tian +1

Given a smooth closed $n$ -manifold $M$ and a $I^º$ -tuple of basepoints $q \subset M$ , we define a Morse-type $A_{\infty}$ -algebra $C M_{-*} (I^c ◯ (M, q))$ , called t…

Higher-dimensional Heegaard Floer homology and spectral networks

Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras

Towards a symplectic Khovanov homology for links in fibered 3-manifolds

Homology of Yang-Baxter modules

Morse theory of loop spaces and Hecke algebras

Towards a symplectic Khovanov homology for links in fibered $3$ -manifolds