SKEIN MODULES AND CHARACTER VARIETIES OF SEIFERT MANIFOLDS

Renaud Detcherry; Efstratia Kalfagianni; Adam S. Sikora

doi:10.1090/btran/239

SKEIN MODULES AND CHARACTER VARIETIES OF SEIFERT MANIFOLDS

Renaud Detcherry
, Efstratia Kalfagianni
, Adam S. Sikora

Mathematics

Université de Bourgogne
Michigan State University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	1264-1288
Number of pages	25
Journal	Transactions of the American Mathematical Society Series B
Volume	12
DOIs	https://doi.org/10.1090/btran/239
State	Published - 2025

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

author = "Renaud Detcherry and Efstratia Kalfagianni and Sikora, \{Adam S.\}",

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AU - Kalfagianni, Efstratia

AU - Sikora, Adam S.

PY - 2025

Y1 - 2025

N2 - We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold M is finitely generated over ℤ[A±1] if and only if M is irreducible and non-Haken. We analyze in detail the character varieties X (M) of such manifolds and show that under mild conditions they are reduced. We compute the Kauffman bracket skein modules for these 3-manifolds (over ℚ(A)) and show that their dimensions coincide with |X (M)|.

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

UR - https://www.scopus.com/pages/publications/105025724211

U2 - 10.1090/btran/239

DO - 10.1090/btran/239

M3 - Article

AN - SCOPUS:105025724211

SN - 2330-0000

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EP - 1288

JO - Transactions of the American Mathematical Society Series B

JF - Transactions of the American Mathematical Society Series B

ER -

SKEIN MODULES AND CHARACTER VARIETIES OF SEIFERT MANIFOLDS

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