最优半耦合的奇点拓扑
Topology of Singularities of Optimal Semicouplings
摘要：
研究了不等维$c$ -最优半耦合的奇点拓扑。我们的主要结果描述了从源空间$(X,σ)$到$c$ -最优半耦合的奇点$Z_j$，$j\geq 0$的同伦约化，只要$(Y, τ)$是黎曼目标空间，$c$是$X\times Y$上的代价，满足一些一般假设（A0）-（A5）.我们构造了连续强形变收缩核$X\leadsto Z_j$，只要沿适当的子集满足均匀半空间（UHS）条件。本文总结了作者博士论文（2019）的一些结果。
英文摘要：
We study the topology of singularities of $c$-optimal semicouplings in unequal dimension. Our main results describe homotopy-reductions from a source space $(X,σ)$ onto the singularities $Z_j$, $j\geq 0$ of $c$-optimal semicouplings whenever $(Y, τ)$ is a Riemannian target space and $c$ is a cost on $X\times Y$ satisfying some general assumptions (A0)--(A5). We construct continuous strong deformation retracts $X\leadsto Z_j$ whenever a condition called Uniform Halfspace (UHS) condition is satisfied along appropriate subsets. This article summarizes some results from the author's PhD thesis (2019).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
