Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Chen, Runze, Guan, Yuanxin, Lü, Zhi
Institution: Fudan University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 等变流形的代数拓扑及相关问题研究
OpenAlex ID: W7214193793