Xiao Chen

collaborators

4 papers

math.GT2026

Minimal Filling $K$ -Systems of Curves

Hong Chang, Xiao Chen, Wujie Shen

In this paper, we determine the exact minimal number of curves in a filling $k$ -system on an oriented surface of genus $g$ for any positive integers $k$ and $g$ .

math.GT2026

A Linear Bound on the Diameter of the Kakimizu Complex for Hyperbolic Knots

Xiao Chen, Wujie Shen

This paper focuses on the Kakimizu complex of a hyperbolic knot $K$ . We define a complex $I S_{ℓ} (K)$ to study incompressible Seifert surfaces of genus at most $ℓ$ , and prove th…

math.GT2025

Uniqueness of Maximal Curve Systems on Punctured Projective Planes

Xiao Chen, Wujie Shen

We show that the maximal $1$ -system of loops in a punctured projective plane is unique up to the mapping class group action if and only if the number of punctures is at most five.

math.GT2025

Systems of curves on non-orientable surfaces

Xiao Chen

We show that the order of the cardinality of maximal complete $1$ -systems of loops on non-orientable surfaces is $\sim ∣ I ¨ ∣^{2}$ . In particular, we determine the exact cardinality…

Minimal Filling K-Systems of Curves

A Linear Bound on the Diameter of the Kakimizu Complex for Hyperbolic Knots

Uniqueness of Maximal Curve Systems on Punctured Projective Planes

Systems of curves on non-orientable surfaces

Minimal Filling $K$ -Systems of Curves