arXiv subjects

Chunxing Yan

Publications and source records attributed to Chunxing Yan.

3 recordsLinked to original sources

arXiv2026

Unbounded Gaps Between Ordinary and Equivariant Dehn Surgery Numbers

For a closed oriented $3$-manifold $Y$ and an orientation-preserving involution $\tau$, let $\DS(Y)$ denote the minimum number of components in an integral surgery description of $Y$, and let $\EDS(Y,\tau)$ denote the corresponding minimum among periodic surgery descriptions inducing $\tau$. We prove that for every integer $k\geq 1$ there is a pair $(Y_k,\tau_k)$ such that \[ \DS(Y_k)=k, \qquad \EDS(Y_k,\tau_k)=2k. \] Consequently, the difference $\EDS(Y,\tau)-\DS(Y)$ is unbounded even when $\tau$ is an involution. This answers Problems~1.15(b) and~1.15(c) in the K3 problem list. We also construct infinitely many pairwise nonhomeomorphic irreducible lens spaces $Z$ admitting involutions $\sigma$ for which \[ \DS(Z)<\EDS(Z,\sigma). \]

math.GT↗

arXiv2026

Some experimental results on stable equivalence of GST Links for the Generalized Property R Conjecture

Gompf-Scharlemann-Thompson and Meier-Zupan constructed an infinite family of R-links that are potential counterexamples of the generalized property R conjecture. Their works also show that whether these links are stably handleslide trivial is an interesting open problem related to the Slice-Ribbon conjecture. In this work, we implement an algorithm to construct all these links explicitly, the details of this algorithm will the content of another paper. With such an algorithm, the stable handleslide triviality of some of these links is verified. Moreover, many links are shown to be stably handleslide equivalent. Some of the results are obtained independently in \cite{Knots in the fiber}

math.GT↗

arXiv2024

Exploring the Potential of Quantum Approximate Optimization Algorithm in Tackling the Perfect Domination Problem

Perfect Domination Problem (PDP), a canonical challenge in combinatorial optimization, finds critical applications in real-world systems such as error-correcting codes, wireless communication networks, and social networks. Decades of research have firmly established its NP-completeness across numerous graph classes. Motivated by rapid advances in quantum computing, significant effort has recently been directed toward quantum algorithms for NP-complete problems, most notably the Quantum Approximate Optimization Algorithm (QAOA). Nonetheless, the applicability and efficacy of quantum approaches to the PDP remain entirely unexplored. This paper initiates the first systematic investigation of the PDP via QAOA. We evaluate solution quality on three benchmark instances of 6, 7, and 8 vertices using 15-18 qubits on a quantum simulator, examining more than 400 distinct parameter configurations. Experimental results confirm the algorithm's effectiveness and expose discernible trends in parameter selection. These outcomes substantiate QAOA's viability for the PDP and mark a seminal step toward situating this classical problem within the quantum-computing paradigm.

quant-ph↗