57 citations · 146 across the 19 of their papers we have counts for
19 papers
A polynomial invariant of planar curves
Zhiyun Cheng, Yin Tian, Tianyu Yuan
We construct a polynomial invariant of planar curves via skein relations, which generalizes Arnold's numerical invariant .
Obstructions to smoothing orbicurves and Orbifold Hecke algebras
Ko Honda, Roman Krutowski, Yin Tian +1
In this paper, we study obstructions to smoothing nodal orbicurves with orbighosts mapped into cyclic quotient singularities. As an application, we show, under some assumptions, th…
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…
Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups II
Lingrui Jiang, Si-qi Liu, Yingchao Tian +1
This is a sequel to arXiv:2506.13656, in which an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups is presented.…
Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups I
Lingrui Jiang, Si-Qi Liu, Yingchao Tian +1
We present an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups, and prove that their monodromy groups are parabo…
An example of higher-dimensional Heegaard Floer homology
Yin Tian, Tianyu Yuan
We count pseudoholomorphic curves in the higher-dimensional Heegaard Floer homology of disjoint cotangent fibers of a two dimensional disk. We show that the resulting algebra is is…
String Condensations in 3+1D and Lagrangian Algebras
Jiaheng Zhao, Jia-Qi Lou, Zhi-Hao Zhang +3
We present three Lagrangian algebras in the modular 2-category associated to the 3+1D topological order and discuss their physical interpretations, connecting algebr…
Higher-dimensional Heegaard Floer homology and Hecke algebras
Ko Honda, Yin Tian, Tianyu Yuan
Given a closed oriented surface of genus greater than 0, we construct a map from the higher-dimensional Heegaard Floer homology of the cotangent fibers of …
Defects in the 3-dimensional toric code model form a braided fusion 2-category
Liang Kong, Yin Tian, Zhi-Hao Zhang
It was well known that there are -particles and -strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional topologica…
Applications of higher-dimensional Heegaard Floer homology to contact topology
Vincent Colin, Ko Honda, Yin Tian
The goal of this paper is to set up the general framework of higher-dimensional Heegaard Floer homology, define the contact class, and use it to give an obstruction to the Liouvill…
The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory
Liang Kong, Yin Tian, Shan Zhou
In this work, for a finite group and a 4-cocycle , we compute explicitly the center of the monoidal 2-category of -…
Towards functor exponentiation
Mikhail Khovanov, Yin Tian
We consider a possible framework to categorify the exponential map exp(-f) given the categorification of a generator f of by Lauda. In this setup the Taylor expansion…
Towards a categorical boson-fermion correspondence
Yin Tian
We construct the Heisenberg counterpart of a Clifford categorification. It is a modification of Khovanov's Heisenberg categorification. We express generators of the Heisenberg cate…
How to categorify the ring of integers localized at two
Mikhail Khovanov, Yin Tian
We construct a triangulated monoidal Karoubi closed category with the Grothendieck ring, naturally isomorphic to the ring of integers localized at two.
Contact categories of disks
Ko Honda, Yin Tian
In the first part of the paper we associate a pre-additive category to a closed oriented surface , called the {\em contact category} and constructed from contac…
A categorification of the square root of -1
Yin Tian
We give a graphical calculus for a monoidal DG category whose Grothendieck group is isomorphic to the ring . We construct a categorical action of $…
A diagrammatic categorification of a Clifford algebra
Yin Tian
We give a graphical calculus for a categorification of a Clifford algebra and its Fock space representation via differential graded categories. The categorical action is motivated…
A categorification of U_T sl(1,1) and its tensor product representations
Yin Tian
We define the Hopf superalgebra U_T sl(1,1), which is a variant of the quantum supergroup U_q sl(1,1), and its tensor product representations V_1^{\otimes n} for n>0. We construct…
A categorification of U_q sl(1,1) as an algebra
Yin Tian
We construct families of differential graded algebras R and R \boxtimes R and give an algebraic formulation of the contact category of a disk through the differential graded catego…