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On dual unit balls of Thurston norms

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.
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Contributor : Abdoul Karim Sane <>
Submitted on : Thursday, July 9, 2020 - 11:03:00 PM
Last modification on : Tuesday, November 24, 2020 - 4:00:18 PM


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  • HAL Id : hal-02537133, version 2
  • ARXIV : 2004.04407



Abdoul Karim Sane. On dual unit balls of Thurston norms. 2020. ⟨hal-02537133v2⟩



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