Yi Liu

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math.GT2025

Deforming abelian elliptic $SL (2, R)$ --representations of knot groups

Yi Liu

The following criterion is proved in this paper. If the Alexander polynomial of a knot $K \subset S^{3}$ has a zero of odd order on the complex unit circle, then there exists a contin…

math.GT2025

On the Euler class one conjecture for fillable contact structures

Yi Liu

In this paper, it is proved that every oriented closed hyperbolic $3$ --manifold $N$ admits some finite cover $M$ with the following property. There exists some even lattice point $…

math.GT2024

A criterion for virtual Euler class one

Yi Liu

Let $M$ be an oriented closed hyperbolic $3$ --manifold. Suppose that $w$ is a rational second cohomology class of $M$ with dual Thurston norm $1$ . Upon the existence of certain non…

math.GT2024

Entropy versus volume via Heegaard diagrams

Yi Liu

The following inequalities are established, improving a former inequality due to Kojima. For any closed arithmetic hyperbolic $3$ --manifold fibering over a circle, the entropy of t…

Deforming abelian elliptic SL(2,R)--representations of knot groups

On the Euler class one conjecture for fillable contact structures

A criterion for virtual Euler class one

Entropy versus volume via Heegaard diagrams

Deforming abelian elliptic $SL (2, R)$ --representations of knot groups