发表机构
Hokkaido University（北海道大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究拓扑线排列补集拓扑，用同调方法证其补集上同调环同构于Orlik - Solomon代数，还研究补集同伦型，发现辛线排列补集有特定同伦型，且拓扑线排列组合类型的补集有多种非同伦等价情况。
AI 中文摘要
拓扑线排列是复射影平面中嵌入球面的一种排列，它在拓扑上推广了复直线排列。本文建立了关于拓扑线排列补集拓扑的基础结果。首先，证明补集的上同调环同构于经典复直线排列的Orlik - Solomon代数，因经典方法不可用，采用同调方法计算上同调环。接着研究补集的同伦型，证明辛线排列的补集具有最小CW复形的同伦型，而拓扑线排列可实现的每种组合类型都有非最小补集的实现，且每种此类组合类型都有无穷多个补集两两非同伦等价的实现。
英文摘要
A topological line arrangement is an arrangement of embedded spheres in the complex projective plane that topologically generalizes a complex line arrangement. In this paper, we establish foundational results on the topology of the complement of topological line arrangements. First, we prove that the cohomology ring of the complement is isomorphic to the Orlik-Solomon algebra, as for classical complex line arrangements. We then study the homotopy type of the complement. We prove that the complement of a symplectic line arrangement has the homotopy type of a minimal CW complex. In contrast, every combinatorial type realizable by a topological line arrangement admits a realization with a non-minimal complement. Moreover, every such combinatorial type admits infinitely many realizations whose complements are pairwise non-homotopy equivalent.
Comments20 pages, 3 figures, the second proof for Theorem 1.1 added
