Equivariant bordism rigidity for toric manifolds

Runze Chen; Yuanxin Guan; Zhi Lü

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arXiv · 2609.27412

Equivariant bordism rigidity for toric manifolds

Runze Chen·Yuanxin Guan·Zhi Lü

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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.

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BibTeX RIS

Runze Chen, Yuanxin Guan, Zhi Lü. 2026-09-23. Equivariant bordism rigidity for toric manifolds. https://arxiv.org/abs/2609.27412

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