Zhenkun Li

activity

20202025

most citedInstanton Floer homology, sutures, and Heegaard diagrams

17 citations · 41 across the 14 of their papers we have counts for

collaborators

14 papers

math.GT2025

Instanton 2-torsion and fibered knots

Deeparaj Bhat, Zhenkun Li, Fan Ye

We prove that the unreduced singular instanton homology $I^{♯} (Y, K; Z)$ has $2$ -torsion for any null-homologous fibered knot $K$ of genus $g > 0$ in a closed $3$ -manifold…

math.GT2025

Instanton dimensions of knot surgeries over arbitrary fields

Zhenkun Li, Fan Ye

Suppose $K \subset S^{3}$ is a knot and suppose $p$ and $q$ are co-prime integers with $q \geq 1$ . For any field $K$ , we establish a dimension formula for the framed instanton…

math.GT2025

Instanton 2-torsion and Dehn surgeries

Zhenkun Li, Fan Ye

In our earlier work on $2$ -torsion in instanton Floer homology, we considered only integral surgeries on a knot $K \subset S^{3}$ and showed that the absence of $2$ -torsion forces $K$ …

math.GT2024

On Legendrian representatives of non-fibered knots

Zhenkun Li, Shunyu Wan

We show that in $(S^{3}, ξ_{s t d})$ if $K$ is a non-trivial knot that realizes the three-dimensional Thurston-Bennequin bound (i.e. $K$ has a Legendrian representative $Λ$ with $tb(Λ)-…

math.GT2024

2-torsion in instanton Floer homology

Zhenkun Li, Fan Ye

This paper studies the existence of $2$ -torsion in instanton Floer homology with $Z$ coefficients for closed $3$ -manifolds and singular knots. First, we show that the non-…

math.GT2022★ 2 cited

Knot surgery formulae for instanton Floer homology II: applications

Zhenkun Li, Fan Ye

This is a companion paper to earlier work of the authors, which proved an integral surgery formula for framed instanton homology. First, we present an enhancement of the large surg…

math.GT2022★ 1 cited

Guts of nearly fibered knots

Zhenkun Li, Fan Ye

The guts of a knot is an invariant defined for the knot complement by Agol-Zhang. Nearly fibered knots, which are defined as knots whose Floer homology has dimension two in the top…

math.GT2022

Knot surgery formulae for instanton Floer homology I: the main theorem

Zhenkun Li, Fan Ye

We prove an integral surgery formula for framed instanton homology $I^{♯} (Y_{m} (K))$ for any knot $K$ in a $3$ -manifold $Y$ with $[K] = 0 \in H_{1} (Y; Q)$ and $m \neq = 0$ . Though…

math.GT2021★ 5 cited

Small Dehn surgery and SU(2)

John A. Baldwin, Zhenkun Li, Steven Sivek +1

We prove that the fundamental group of 3-surgery on a nontrivial knot in the 3-sphere always admits an irreducible SU(2)-representation. This answers a question of Kronheimer and M…

math.GT2021★ 2 cited

SU(2) representations and a large surgery formula

Zhenkun Li, Fan Ye

A knot $K \subset S^{3}$ is called $S U (2)$ -abundant if it satisfies two conditions: first, for all but finitely many $r \in Q \ {0}$ , there exists an irreducible repre…

math.GT2021★ 8 cited

An enhanced Euler characteristic of sutured instanton homology

Zhenkun Li, Fan Ye

For a balanced sutured manifold $(M, γ)$ , we construct a decomposition of $S H I (M, γ)$ with respect to torsions in $H = H_{1} (M; Z)$ , which generalizes the decomposition of $I^\sh…

math.GT2021★ 6 cited

Instanton Floer homology, sutures, and Euler characteristics

Zhenkun Li, Fan Ye

This is a companion paper to an earlier work of the authors. In this paper, we provide an axiomatic definition of Floer homology for balanced sutured manifolds and prove that the g…

math.GT2020

Sutured instanton homology and Heegaard diagrams

John A. Baldwin, Zhenkun Li, Fan Ye

Suppose H is an admissible Heegaard diagram for a balanced sutured manifold (M,γ). We prove that the number of generators of the associated sutured Heegaard Floer complex is an upp…

math.GT2020★ 17 cited

Instanton Floer homology, sutures, and Heegaard diagrams

Zhenkun Li, Fan Ye

This paper establishes a new technique that enables us to access some fundamental structural properties of instanton Floer homology. As an application, we establish, for the first…