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Peer-reviewedCC BY 4.0Annales Henri Lebesgue

A Poincaré-Lefschetz Theorem for Cellular Cosheaves and an Application to the Tropical Homology of Orbifold Toric Varieties

  • Jules Chenal
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Abstract

We begin by presenting a version of the Poincaré–Lefschetz theorem for certain cellular cosheaves on a particular subdivision of a CW-complex K. To that end we construct a cellular sheaf on K whose cohomology with compact support is isomorphic to the homology of the initial cosheaf. Thereafter we use the first result to generalise the tropical version of the Lefschetz Hyperplane Section Theorem to some singular tropical toric varieties and singular tropical hypersurfaces.

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Cite

BibTeXRIS
BibTeX
@article{chenal2026poincarélefschetz,
  title = {{A Poincaré-Lefschetz Theorem for Cellular Cosheaves and an Application to the Tropical Homology of Orbifold Toric Varieties}},
  author = {Jules Chenal},
  journal = {Annales Henri Lebesgue},
  year = {2026},
  month = oct,
  doi = {10.5802/ahl.236},
  url = {https://hal.science/hal-04164269v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Poincaré-Lefschetz Theorem for Cellular Cosheaves and an Application to the Tropical Homology of Orbifold Toric Varieties
AU  - Jules Chenal
PY  - 2026
DA  - 2026/10/16
JO  - Annales Henri Lebesgue
DO  - 10.5802/ahl.236
UR  - https://hal.science/hal-04164269v2
AB  - We begin by presenting a version of the Poincaré–Lefschetz theorem for certain cellular cosheaves on a particular subdivision of a CW-complex K. To that end we construct a cellular sheaf on K whose cohomology with compact support is isomorphic to the homology of the initial cosheaf. Thereafter we use the first result to generalise the tropical version of the Lefschetz Hyperplane Section Theorem to some singular tropical toric varieties and singular tropical hypersurfaces.
SN  - 2644-9463
ER  -