arXiv subjects

Jingling Yang

Publications and source records attributed to Jingling Yang.

6 recordsLinked to original sources

arXiv2026

Local Knots, $\nu^+$-Sharp Knots, and Rational Slice Genus

Hom and Wu introduced the knot concordance invariant $\nu^{+}$ for knots in $S^{3}$ and proved that it gives a lower bound for the slice genus. Wu and Yang extended $\nu^{+}$ to knots in rational homology $3$-spheres, where it gives a lower bound for the rational slice genus, an analogue of the slice genus for knots in rational homology $3$-spheres. We call a knot $\nu^{+}$-sharp if this bound is realized as an equality. An open question asks whether a local knot in a $3$-manifold $Y$, that is, a knot contained in a $3$-ball, can bound a surface of smaller genus in $Y\times I$ than in $S^{3}\times I$. Using the Heegaard Floer invariant $\nu^+$, we show that this does not occur for local knots arising from $\nu^+$-sharp knots: if $K\subset S^3$ is $\nu^+$-sharp and $Y$ is a rational homology $3$-sphere, then the induced local knot in $Y$ has rational slice genus equal to the slice genus of $K$. The proof proceeds by establishing an additivity result for the rational slice genus.

math.GT↗

arXiv2025

Surgeries between lens spaces of type $L(n,1)$ and the Heegaard Floer $d$-invariant

We establish a $d$-invariant surgery formula for $L$-space knots that provides an effective tool for studying surgeries between lens spaces. Using this formula, we classify distance one surgeries between lens spaces of the form $L(n,1)$. This classification has direct applications to band surgeries between torus links $T(2,n)$, with connections to DNA topology. In particular, we show that chirally cosmetic banding of torus links can possibly occur only when $n=1,5,9$ or $10$.

math.GT↗

arXiv2023

Rational genus and Heegaard Floer homology

Turaev defined a function on the first homology of a rational homology 3-sphere $Y$ as the minimal rational Seifert genus of all knots in this homology class. Ni and the first author discovered a lower bound of this function using the Heegaard Floer $d$-invariant and showed that Floer simple knots are rational Seifert genus minimizers. In this paper, we give a simple reproof of the above results. We then define a version of rational slice genus for knots in the product 4-manifold $Y\times I$ and investigate the analogous minimal genus problem. We prove the same lower bound in terms of the $d$-invariant formula and the same genus minimizers given by Floer simple knots.

math.GT↗

arXiv2021

Distance one surgeries on the lens space $L(n,1)$

In this paper, we show that the lens space $L(s,1)$ for $s \neq 0 $ is obtained by a distance one surgery along a knot in the lens space $L(n,1)$ with $n \geq 5$ odd only if $n$ and $s$ satisfy one of the following cases: (1) $n \geq 5$ is any odd integer and $s=\pm 1, n, n \pm 1$ or $n \pm 4$; (2) $n=5$ and $s=-5$; (3) $n=5$ and $s=-9$; (4) $n=9$ and $s=-5$. As a corollary, we prove that the torus link $T(2,s)$ for $s \neq 0 $ is obtained by a band surgery from $T(2,n)$ with $n \geq 5$ odd only if $n$ and $s$ are as listed above. Combined with the result of Lidman, Moore and Vazquez, it immediately follows that the only nontrivial torus knot $T(2,n)$ admitting chirally cosmetic banding is $T(2,5)$. The key ingredient of our proof is the Heegaard Floer mapping cone formula.

math.GT↗

arXiv2021

Studies of distance one surgeries on the lens space $L(p,1)$

In this paper, we study distance one surgeries between lens spaces $L(p,1)$ with $p \geq 5$ prime and lens spaces $L(n,1)$ for $n \in \mathbb{Z}$ and band surgeries from $T(2,p)$ to $T(2,n)$. In particular, we prove that $L(n,1)$ is obtained by a distance one surgery from $L(5,1)$ only if $n=\pm 1$, $4$, $\pm 5$, $6$ or $\pm 9$, and $L(n,1)$ is obtained by a distance one surgery from $L(7,1)$ if and only if $n=\pm 1$, $3$, $6$, $7$, $8$ or $11$.

math.GT↗

arXiv2017

Non-hyperbolic solutions to tangle equations involving composite links

Solving tangle equations is deeply connected with studying enzyme action on DNA. The main goal of this paper is to solve the system of tangle equations $N(O+X_1)=b_1$ and $N(O+X_2)=b_2 \# b_3$, where $X_1$ and $X_2$ are rational tangles, and $b_i$ is a 2-bridge link, for $i=1,2,3$, with $b_2$ and $b_3$ nontrivial. We solve this system of equations under the assumption $\widetilde{O}$, the double branched cover of $O$, is not hyperbolic, i.e.$O$ is not $π$-hyperbolic. Besides, we also deal with tangle equations involving 2-bridge links only under the assumption $O$ is an algebraic tangle.

math.GT↗