Zhenkun Li

collaborators

7 papers

math.GT2026

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.GT2026

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.GT2026

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.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

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.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…