Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 6, 1965–2352
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Punctured JSJ tori and tautological extensions of Azumaya algebras

Yi Wang

Algebraic & Geometric Topology 26 (2026) 2049–2077
Bibliography
1 M Aschenbrenner, S Friedl, H Wilton, 3-manifold groups, European Mathematical Society (EMS), Zürich (2015) MR3444187
2 C Ashley, J P Burelle, S Lawton, Rank 1 character varieties of finitely presented groups, Geom. Dedicata 192 (2018) 1 MR3749420
3 J A Baldwin, S Sivek, Zero-surgery characterizes infinitely many knots, Math. Res. Lett. 31 (2024) 1639 MR4862352
4 S Boyer, E Luft, X Zhang, On the algebraic components of the SL(2, ) character varieties of knot exteriors, Topology 41 (2002) 667 MR1905834
5 S Boyer, X Zhang, A proof of the finite filling conjecture, J. Differential Geom. 59 (2001) 87 MR1909249
6 E Chesebro, S Tillmann, Not all boundary slopes are strongly detected by the character variety, Comm. Anal. Geom. 15 (2007) 695 MR2395254
7 T Chinburg, A W Reid, M Stover, Azumaya algebras and canonical components, Int. Math. Res. Not. 2022 (2022) 4969 MR4403955
8 J L Colliot-Thélène, Birational invariants, purity and the Gersten conjecture, from: "K-theory and algebraic geometry : connections with quadratic forms and division algebras" (editors B Jacob, A Rosenberg), Proc. Sympos. Pure Math. 58.1, Amer. Math. Soc. (1995) 1 MR1327280
9 D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of 3-manifolds, Invent. Math. 118 (1994) 47 MR1288467
10 M Culler, Lifting representations to covering groups, Adv. in Math. 59 (1986) 64 MR825087
11 M Culler, P B Shalen, Varieties of group representations and splittings of 3-manifolds, Ann. of Math. (2) 117 (1983) 109 MR683804
12 M Culler, P B Shalen, Bounded, separating, incompressible surfaces in knot manifolds, Invent. Math. 75 (1984) 537 MR735339
13 R J Daverman, R B Sher, editors, Handbook of geometric topology, North-Holland, Amsterdam (2002) MR1886666
14 N M Dunfield, Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds, Topology 38 (1999) 457 MR1660313
15 D Gabai, Foliations and the topology of 3-manifolds, III, J. Differential Geom. 26 (1987) 479 MR910018
16 C M Gordon, J Luecke, Dehn surgeries on knots creating essential tori, II, Comm. Anal. Geom. 8 (2000) 671 MR1792371
17 A Grothendieck, Le groupe de Brauer, III : Exemples et compléments, from: "Dix exposés sur la cohomologie des schémas", North-Holland (1968) 88 MR0244271
18 Y Harpaz, O Wittenberg, The Massey vanishing conjecture for number fields, Duke Math. J. 172 (2023) 1 MR4533716
19 A Hatcher, W Thurston, Incompressible surfaces in 2-bridge knot complements, Invent. Math. 79 (1985) 225 MR778125
20 K Ichihara, H Masai, Exceptional surgeries on alternating knots, Comm. Anal. Geom. 24 (2016) 337 MR3514563
21 W Jaco, Lectures on three-manifold topology, 43, Amer. Math. Soc. (1980) MR565450
22 W Jaco, P B Shalen, Seifert fibered spaces in 3-manifolds, from: "Geometric topology" (editor J C Cantrell), Academic Press, New York (1979) 91 MR537728
23 T Kitano, Reidemeister torsion of Seifert fibered spaces for SL(2; )-representations, Tokyo J. Math. 17 (1994) 59 MR1279569
24 S Lang, Survey of diophantine geometry, Springer (1997)
25 M L Macasieb, K L Petersen, R M van Luijk, On character varieties of two-bridge knot groups, Proc. Lond. Math. Soc. (3) 103 (2011) 473 MR2827003
26 C Maclachlan, A W Reid, The arithmetic of hyperbolic 3-manifolds, 219, Springer (2003) MR1937957
27 P Menal-Ferrer, J Porti, Twisted cohomology for hyperbolic three manifolds, Osaka J. Math. 49 (2012) 741 MR2993065
28 J S Milne, Étale cohomology, 33, Princeton Univ. Press (1980) MR559531
29 L Paoluzzi, J Porti, Conway spheres as ideal points of the character variety, Math. Ann. 354 (2012) 707 MR2965258
30 R M Patton, Incompressible punctured tori in the complements of alternating knots, Math. Ann. 301 (1995) 1 MR1312568
31 K Petersen, A Reid, Gonality and genus of canonical components of character varieties, from: "Characters in Low-Dimensional Topology" (editors O Collin, S Friedl, C Gordon, S Tillmann, L Watson), Contemporary Mathematics 760, Amer. Math. Soc. (2020) 263
32 S Schleimer, Introduction to towers in topology, preprint (2018)
33 N Sekino, Generalized torsion elements in the fundamental groups of 3-manifolds obtained by 0-surgeries along some double twist knots, Topology Appl. 343 (2024) 108798 MR4685211
34 J P Serre, Local fields, 67, Springer (1979) MR554237
35 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
36 S Tillmann, Character varieties of mutative 3-manifolds, Algebr. Geom. Topol. 4 (2004) 133 MR2059186
37 S Tillmann, Degenerations of ideal hyperbolic triangulations, Math. Z. 272 (2012) 793 MR2995140
38 Y Tsutsumi, Universal bounds for genus one Seifert surfaces for hyperbolic knots and surgeries with non-trivial JSJT-decompositions, Interdiscip. Inform. Sci. 9 (2003) 53 MR2023107
39 L G Valdez-Sánchez, Seifert surfaces for genus one hyperbolic knots in the 3-sphere, Algebr. Geom. Topol. 19 (2019) 2151 MR4023316
40 Y Wang, Limiting characters at ideal points detecting twice-punctured tori (2025) arXiv:2404.06388