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On dual unit balls of Thurston norms

By Abdoul Karim SANE

Abstract

Thurston norms are invariants of 3-manifolds defined on their se- cond homology vector spaces, and understanding the shape of their dual unit ball is a (widely) open problem. W. Thurston showed that every symmetric polygon in Z^2, whose vertices satisfy a parity property, is the dual unit ball of a Thurston norm on a 3-manifold. However, it is not known if the parity property on the vertices of polytopes is a sufficient condition in higher dimension or if their are polytopes, with mod 2 congruent vertices, that cannot be realized as dual unit balls of Thurston norms. In this article, we provide a family of polytopes in Z^2g that can be realized as dual unit balls of Thurston norms on 3- manifolds. These polytopes come from intersection norms on oriented closed surfaces and this article widens the bridge between these two norms

Topics: Incompressible surface, Thurston norm, Intersection norm, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]
Publisher: HAL CCSD
Year: 2020
OAI identifier: oai:HAL:hal-02537133v2
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