发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出等变配边方法，证明环面流形同构等价于弱等变酉配边，并给出全定向拟环面流形的刚性结果，以拓扑框架检测几何与组合刚性。
AI 中文摘要
本文发展了一种基于配边理论的方法，用于研究环面流形与拟环面流形的刚性（rigidity）问题。我们证明了两个环面流形作为代数簇同构当且仅当它们是弱等变酉配边（weakly equivariantly unitary bordant）的。我们还为满足单射性条件（injectivity condition）的全定向拟环面流形（omnioriented quasitoric manifolds）建立了一个平行的刚性结果，表明它们的等变酉配边类完全决定了其保持全定向的等变同胚类型。因此，等变配边为检测几何与组合刚性提供了一个拓扑框架。
英文摘要
In this paper, we develop a bordism-theoretic approach to rigidity problems for toric and quasitoric manifolds. We prove that two toric manifolds are isomorphic as varieties if and only if they are weakly equivariantly unitary bordant. We also establish a parallel rigidity result for omnioriented quasitoric manifolds satisfying the injectivity condition, showing that their equivariant unitary bordism classes completely determine their omniorientation-preserving equivariant homeomorphism types. Thus, equivariant bordism provides a topological framework for detecting geometric and combinatorial rigidity.
Comments17 pages. Comments are welcome!
