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Spaces with Multiple Conical Singularities and their Stratifications

  • Mohammad Alattar
  • Lewis Tadman
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Abstract

In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and that in fact, the intrinsic stratification agrees with the MCS stratification. As a consequence, we improve on Perelman's result and answer affirmatively a question by Fujioka.

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Cite

BibTeXRIS
BibTeX
@misc{alattar2026spaces,
  title = {{Spaces with Multiple Conical Singularities and their Stratifications}},
  author = {Mohammad Alattar and Lewis Tadman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.01119},
  eprint = {2606.01119},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.01119},
}
RIS
TY  - UNPB
TI  - Spaces with Multiple Conical Singularities and their Stratifications
AU  - Mohammad Alattar
AU  - Lewis Tadman
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2606.01119
UR  - https://arxiv.org/abs/2606.01119
AB  - In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and that in fact, the intrinsic stratification agrees with the MCS stratification. As a consequence, we improve on Perelman's result and answer affirmatively a question by Fujioka.
ER  -