{
  "abstract": "We study regular spherical actions, namely, actions of a connected compact Lie group G on a manifold M with equidimensional orbits, some of which are spheres. These spherical orbits are diffeomorphic to homogeneous spaces G/H, and there is a list of nine possible families of pairs (G, H). The normalizer N of H in G plays an important role in our calculations, as does the Weyl group W = N/H. In fact, there are three possibilities for W, namely: Z_2, S^1 and S^3. The goal of this paper is to relate the cohomology of M to that of the orbit space M/G. We obtain a particularly simple relationship in the first case, W = Z_2. For the remaining two cases, W = S^1 and W = S^3, it is already known that the cohomology of M and that of the orbit space M/G are related by the Gysin sequence ... \\to H^k(M/G) \\to H^k(M ) \\to H^{k-d}(M/G) \\to H^{k+1}(M/G) \\to ... In this work, we provide a direct construction of this sequence, avoiding the use of spectral sequences. Moreover, we give an explicit description of the connecting homomorphism as multiplication by a power of the Euler class associated with the action of the Weyl group W = S^l on the fixed-point set M^H.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02111",
  "author_total": 3,
  "authors": [
    {
      "name": "José Ignacio Royo Prieto"
    },
    {
      "name": "Martintxo Saralegi-Aranguren"
    },
    {
      "name": "Robert Wolak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0pg06de5t9331.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02111",
  "fulltext_url": null,
  "id": "0pg06de5t9331",
  "issns": [],
  "landing_url": "https://hal.science/hal-05849852v1",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02111",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0pg06de5t9331.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:19Z",
      "native_id": "hal-05849852",
      "source": "hal",
      "url": "https://hal.science/hal-05849852v1"
    },
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02111",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02111"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Cohomology of regular spherical actions",
  "title_text": "Cohomology of regular spherical actions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/0pg06de5t9331",
  "venue": "HAL",
  "versions": []
}