发表机构
Yau Mathematical Sciences Center, Tsinghua University; Beijing International Center for Mathematical Research, Peking University; Department of Mathematics, The University of Maryland at College Park（丘成桐数学科学中心，清华大学; 北京国际数学研究中心，北京大学; 马里兰大学帕克分校数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明 $S^4$ 中任意光滑两分量分离球面链环存在无穷多个拓扑互不同痕的分离 $3$-球面，推广了 Tatsuoka 定理，并建立了适用于连通和的充分条件。
AI 中文摘要
我们证明了 $S^4$ 中每个光滑的两分量分离球面链环 $L\sqcup R\subset S^4$ 都允许无穷多个光滑分离 $3$-球面，这些球面在拓扑上互不同痕。这推广了 Tatsuoka 的一个定理，从两分量球面平凡链环推广到具有任意打结球面分量的分离链环。在证明过程中，我们建立了一个一般充分条件，在该条件下，光滑 $4$-流形的连通和允许无穷多个拓扑上互不同痕的分离 $3$-球面。这一准则可能具有独立的意义；特别是，它适用于所有先前已知的正亏格曲面链环分离 $3$-球面非唯一性的例子。
英文摘要
We prove that every smooth two-component split sphere link $L\sqcup R\subset S^4$ admits infinitely many smooth splitting $3$-spheres that are topologically non-isotopic. This generalizes a theorem of Tatsuoka from the two-component sphere unlink to split links with arbitrarily knotted sphere components. In the course of the proof, we establish a general sufficient condition under which a connected sum of smooth $4$-manifolds admits infinitely many topologically non-isotopic splitting $3$-spheres. This criterion may be of independent interest; in particular, it applies to all previously known examples of nonuniqueness for splitting $3$-spheres of positive-genus surface links.
Comments14 pages, 2 figures. Version 2 proved a slightly more general result and corrected several typos
