Tropical Poincaré duality spaces

Abstract: Itenberg, Katzarkov, Mikhalkin and Zharkov introduced tropical homology and cohomology groups for tropical varieties. These groups are related by a cap product map. When this cap product is an isomorphism, the tropical variety is called a Tropical Poincaré duality (TPD) space. Bergman fans of matroids are TPD spaces by a result of Jell, Smacka and Shaw. In this talk, we give criteria for when a fan is a TPD space at all its faces. Such spaces are called smooth in recent work of Amini and Piquerez, and satisfy certain cohomological restrictions. We also classify TPD spaces of dimension one. We will conclude with some examples and open questions.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

Series comments: Please email one of the organizers to receive login info and join our mail list.