Work

Skein modules and character varieties of Seifert manifolds

Year: 2025

Type: article

Abstract: We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold M M is finitely generated over Z [ A ± 1 ] \mathbb {Z}[A^{\pm 1}] if and only if M M is irreducible and non-Haken. We analyze in detail the character varieties X ( M ) \mathcal {X}(M) of such manifolds and show that under mild conditions they are reduced. We compute the Kauffman bracket skein modules for these 3 3 -manifolds (over Q ( A ) \mathbb {Q}(A) ) and show that their dimensions coincide with | X ( M ) | |\mathcal {X}(M)| .

Source: Transactions of the American Mathematical Society Series B

DOI: 10.1090/btran/239

Authors: Renaud Detcherry, Efstratia Kalfagianni, Adam Sikora

Institutions: Centre National de la Recherche Scientifique, Institut de Mathématiques de Bourgogne, Université Bourgogne Franche-Comté, Michigan State University, University at Buffalo, State University of New York

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,750

Funders: National Science Foundation, Simons Foundation, Agence Nationale de la Recherche