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PreprintCC BY-NC-ND 4.0arXiv

Homotopy rigidity for quasitoric manifolds over a product of simplices

  • Xin Fu
  • Tseleung So
  • Jongbaek Song
  • Stephen Theriault
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Abstract

We consider a variation of the Cohomological Rigidity Problem: whether two quasitoric manifolds whose cohomology rings are isomorphic are homotopy equivalent. We show that if two quasitoric manifolds have isomorphic cohomology rings and the associated polytope of one of them is a product of simplices, then they are homotopy equivalent after localizing away from an explicit list of primes.

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Cite

BibTeXRIS
BibTeX
@misc{fu2026homotopy,
  title = {{Homotopy rigidity for quasitoric manifolds over a product of simplices}},
  author = {Xin Fu and Tseleung So and Jongbaek Song and Stephen Theriault},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04234},
  eprint = {2610.04234},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04234},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Homotopy rigidity for quasitoric manifolds over a product of simplices
AU  - Xin Fu
AU  - Tseleung So
AU  - Jongbaek Song
AU  - Stephen Theriault
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04234
UR  - https://arxiv.org/abs/2610.04234
AB  - We consider a variation of the Cohomological Rigidity Problem: whether two quasitoric manifolds whose cohomology rings are isomorphic are homotopy equivalent. We show that if two quasitoric manifolds have isomorphic cohomology rings and the associated polytope of one of them is a product of simplices, then they are homotopy equivalent after localizing away from an explicit list of primes.
ER  -