dc.date.accessioned | 2024-02-28T17:59:08Z | |
dc.date.available | 2024-02-28T17:59:08Z | |
dc.date.created | 2023-10-18T13:27:07Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Aksnes, Edvard . Tropical Poincaré duality spaces. Advances in Geometry. 2023, 23(3), 345-370 | |
dc.identifier.uri | http://hdl.handle.net/10852/108746 | |
dc.description.abstract | 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 Poincaré 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 Poincaré duality space .
In this article, we first give some necessary conditions for fans to be tropical Poincaré duality spaces and a classification in dimension one. Next, we prove that tropical Poincaré duality for the stars of all faces of dimension greater than zero and a vanishing condition implies tropical Poincaré duality of the fan. This leads to necessary and sufficient conditions for a fan to be a local tropical Poincaré duality space. Finally, we use such fans to show that certain abstract balanced polyhedral spaces satisfy tropical Poincaré duality. | |
dc.language | EN | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.title | Tropical Poincaré duality spaces | |
dc.title.alternative | ENEngelskEnglishTropical Poincaré duality spaces | |
dc.type | Journal article | |
dc.creator.author | Aksnes, Edvard | |
cristin.unitcode | 185,15,13,55 | |
cristin.unitname | Algebra, geometri og topologi | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.cristin | 2185891 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances in Geometry&rft.volume=23&rft.spage=345&rft.date=2023 | |
dc.identifier.jtitle | Advances in Geometry | |
dc.identifier.volume | 23 | |
dc.identifier.issue | 3 | |
dc.identifier.startpage | 345 | |
dc.identifier.endpage | 370 | |
dc.identifier.doi | https://doi.org/10.1515/advgeom-2023-0017 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 1615-715X | |
dc.type.version | PublishedVersion | |