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- W4308608604 abstract "The tropical fundamental class of a rational balanced polyhedral fan induces cap products between tropical cohomology and tropical Borel-Moore homology. When all these cap products are isomorphisms, the fan is said to be a tropical Poincar'e duality space. If all the stars of faces also are such spaces, such as for fans of matroids, the fan is called a local tropical Poincar'e duality space. In this article, we first give some necessary conditions for fans to be tropical Poincar'e duality spaces and a classification in dimension one. Next, we prove that tropical Poincar'e duality for the stars of all faces of dimension greater than zero and a vanishing condition implies tropical Poincar'e duality of the fan. This leads to necessary and sufficient conditions for a fan to be a local tropical Poincar'e duality space. Finally, we use such fans to show that certain abstract balanced polyhedral spaces satisfy tropical Poincar'e duality." @default.
- W4308608604 created "2022-11-13" @default.
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- W4308608604 date "2021-12-07" @default.
- W4308608604 modified "2023-09-25" @default.
- W4308608604 title "Tropical Poincar'e duality spaces" @default.
- W4308608604 doi "https://doi.org/10.48550/arxiv.2112.03680" @default.
- W4308608604 hasPublicationYear "2021" @default.
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