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PreprintCC BY-NC-SA 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{chen2026equivariant,
  title = {{Equivariant bordism rigidity for toric manifolds}},
  author = {Runze Chen and Yuanxin Guan and Zhi Lü},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.27412},
  eprint = {2609.27412},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27412},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Equivariant bordism rigidity for toric manifolds
AU  - Runze Chen
AU  - Yuanxin Guan
AU  - Zhi Lü
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.27412
UR  - https://arxiv.org/abs/2609.27412
AB  - 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.
ER  -