Algebraic & Geometric Topology Volume 26, issue 3 (2026)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

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

Bibliography

1	N Abdiel, C Frohman, The localized skein algebra is Frobenius, Algebr. Geom. Topol. 17 (2017) 3341 MR3709648
2	J R Aranda, N Ferguson, Generating sets for the Kauffman skein module of a family of Seifert fibered spaces, New York J. Math. 28 (2022) 44 MR4359210
3	J W Barrett, Skein spaces and spin structures, Math. Proc. Cambridge Philos. Soc. 126 (1999) 267 MR1670233
4	D Bullock, Rings of SL₂(ℂ)-characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
5	D Bullock, J H Przytycki, Multiplicative structure of Kauffman bracket skein module quantizations, Proc. Amer. Math. Soc. 128 (2000) 923 MR1625701
6	A Carrega, Nine generators of the skein space of the 3-torus, Algebr. Geom. Topol. 17 (2017) 3449 MR3709652
7	R Detcherry, Infinite families of hyperbolic 3-manifolds with finite-dimensional skein modules, J. Lond. Math. Soc. (2) 103 (2021) 1363 MR4273472
8	P M Gilmer, J M Harris, On the Kauffman bracket skein module of the quaternionic manifold, J. Knot Theory Ramifications 16 (2007) 103 MR2300430
9	S Gunningham, D Jordan, P Safronov, The finiteness conjecture for skein modules, Invent. Math. 232 (2023) 301 MR4557403
10	J Hoste, J H Przytycki, The (2,∞)-skein module of lens spaces ; a generalization of the Jones polynomial, J. Knot Theory Ramifications 2 (1993) 321 MR1238877
11	J Hoste, J H Przytycki, The Kauffman bracket skein module of S¹ × S², Math. Z. 220 (1995) 65 MR1347158
12	T T Q Lê, The colored Jones polynomial and the A-polynomial of knots, Adv. Math. 207 (2006) 782 MR2271986
13	T T Q Le, A T Tran, The Kauffman bracket skein module of two-bridge links, Proc. Amer. Math. Soc. 142 (2014) 1045 MR3148538
14	T T Q Le, A T Tran, On the AJ conjecture for knots, Indiana Univ. Math. J. 64 (2015) 1103 MR3385787
15	J Marché, The skein module of torus knots, Quantum Topol. 1 (2010) 413 MR2733247
16	M Mroczkowski, Kauffman bracket skein module of a family of prism manifolds, J. Knot Theory Ramifications 20 (2011) 159 MR2777022
17	R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
18	J H Przytycki, Kauffman bracket skein module of a connected sum of 3-manifolds, Manuscripta Math. 101 (2000) 199 MR1742248
19	J H Przytycki, A S Sikora, On skein algebras and Sl₂(ℂ)-character varieties, Topology 39 (2000) 115 MR1710996
20	T Saito, M Scharlemann, J Schultens, Lecture notes on generalized Heegaard splittings, (2005) arXiv:math/0504167