Finiteness conjecture for 3-manifolds obtained from handlebodies by attaching 2-handles

Karuo, Hiroaki; Wang, Zhihao

doi:10.2140/agt.2026.26.1095

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ISSN (electronic): 1472-2739

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Finiteness conjecture for 3-manifolds obtained from handlebodies by attaching 2-handles

Hiroaki Karuo and Zhihao Wang

Algebraic & Geometric Topology 26 (2026) 1095–1114

DOI: 10.2140/agt.2026.26.1095

Abstract

We study a generalized Witten’s finiteness conjecture for the skein modules of oriented compact $3$ -manifolds with boundary. We formulate an equivalent version of the generalized finiteness conjecture using handlebodies and 2-handles, and prove the conjecture for some classes with the handlebodies of genus $2$ and $3$ using the equivalent version.

Keywords

skein module, finiteness conjecture

Mathematical Subject Classification

Primary: 57K31

Secondary: 57K20, 57R65

References

Publication

Received: 2 September 2024

Revised: 7 December 2024

Accepted: 30 January 2025

Published: 1 April 2026

Authors

Hiroaki Karuo
Department of Mathematics Gakushuin University Tokyo Japan

Zhihao Wang
School of Mathematics Korea Institute for Advanced Study (KIAS) 85 Hoegi-ro, Dongdaemun-gu, Seoul 02455 South Korea

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Volume 26, issue 3 (2026)