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

Volume 30
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Mutations and faces of the Thurston norm ball dynamically represented by multiple distinct flows

Anna Parlak

Geometry & Topology 29 (2025) 2105–2173
Bibliography
1 I Agol, C C Tsang, Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications, Algebr. Geom. Topol. 24 (2024) 3401 MR4812222
2 T Barbot, Generalizations of the Bonatti–Langevin example of Anosov flow and their classification up to topological equivalence, Comm. Anal. Geom. 6 (1998) 749 MR1652255
3 T Barthelmé, S Frankel, K Mann, Orbit equivalences of pseudo-Anosov flows, Invent. Math. (2025)
4 C Bonatti, I Iakovoglou, Anosov flows on 3-manifolds : the surgeries and the foliations, Ergodic Theory Dynam. Systems 43 (2023) 1129 MR4555824
5 C Bonatti, R Langevin, Un exemple de flot d’Anosov transitif transverse à un tore et non conjugué à une suspension, Ergodic Theory Dynam. Systems 14 (1994) 633 MR1304136
6 B A Burton, The Pachner graph and the simplification of 3-sphere triangulations, from: "Computational geometry", ACM (2011) 153 MR2919606
7 B A Burton, R Budney, W Pettersson, others, Regina: software for low-dimensional topology (1999)
8 M Culler, N M Dunfield, M Goerner, J R Weeks, SnapPy, a computer program for studying the geometry and topology of 3-manifolds
9 N M Dunfield, Alexander and Thurston norms of fibered 3-manifolds, Pacific J. Math. 200 (2001) 43 MR1863406
10 N M Dunfield, S Garoufalidis, A Shumakovitch, M Thistlethwaite, Behavior of knot invariants under genus 2 mutation, New York J. Math. 16 (2010) 99 MR2657370
11 S Fenley, L Mosher, Quasigeodesic flows in hyperbolic 3-manifolds, Topology 40 (2001) 503 MR1838993
12 S Frankel, S Schleimer, H Segerman, From veering triangulations to link spaces and back again, preprint (2019) arXiv:1911.00006
13 D Fried, Fibrations over S1 with pseudo-Anosov monodromy, from: "Travaux de Thurston sur les surfaces" (editors A Fathi, F Laudenbach, V Poénaru), Astérisque 66-67, Soc. Math. France (1979) 251
14 D Fried, The geometry of cross sections to flows, Topology 21 (1982) 353 MR670741
15 D Fried, Transitive Anosov flows and pseudo-Anosov maps, Topology 22 (1983) 299 MR710103
16 S Friedl, W Lück, The L2-torsion function and the Thurston norm of 3-manifolds, Comment. Math. Helv. 94 (2019) 21 MR3941465
17 D Futer, F Guéritaud, Explicit angle structures for veering triangulations, Algebr. Geom. Topol. 13 (2013) 205 MR3031641
18 D Gabai, Foliations and the topology of 3-manifolds, J. Differential Geom. 18 (1983) 445 MR723813
19 D Gabai, Foliations and genera of links, Topology 23 (1984) 381 MR780731
20 A Giannopolous, S Schleimer, H Segerman, A census of veering triangulations, electronic reference (2019)
21 S Goodman, Dehn surgery on Anosov flows, from: "Geometric dynamics", Lecture Notes in Math. 1007, Springer (1983) 300 MR1691596
22 M Handel, W P Thurston, Anosov flows on new three manifolds, Invent. Math. 59 (1980) 95 MR577356
23 C D Hodgson, J H Rubinstein, H Segerman, S Tillmann, Veering triangulations admit strict angle structures, Geom. Topol. 15 (2011) 2073 MR2860987
24 C D Hodgson, J H Rubinstein, H Segerman, S Tillmann, Triangulations of 3-manifolds with essential edges, Ann. Fac. Sci. Toulouse Math. 24 (2015) 1103 MR3485328
25 S Kamatani, H Kodama, T Noda, A Birkhoff section for the Bonatti–Langevin example of Anosov flow, from: "Foliations 2005", World Sci. (2006) 229 MR2284784
26 P Kirk, C Livingston, Concordance and mutation, Geom. Topol. 5 (2001) 831 MR1871406
27 M Lackenby, Taut ideal triangulations of 3-manifolds, Geom. Topol. 4 (2000) 369 MR1790190
28 M Landry, Taut branched surfaces from veering triangulations, Algebr. Geom. Topol. 18 (2018) 1089 MR3773749
29 M P Landry, Veering triangulations and the Thurston norm : homology to isotopy, Adv. Math. 396 (2022) 108102 MR4370465
30 M Landry, Stable loops and almost transverse surfaces, Groups Geom. Dyn. 17 (2023) 35 MR4563328
31 M P Landry, Y N Minsky, S J Taylor, Flows, growth rates, and the veering polynomial, Ergodic Theory Dynam. Systems 43 (2023) 3026 MR4624489
32 M P Landry, Y N Minsky, S J Taylor, A polynomial invariant for veering triangulations, J. Eur. Math. Soc. 26 (2024) 731 MR4705661
33 B Martelli, An introduction to geometric topology, self published (2016)
34 C T McMullen, Polynomial invariants for fibered 3-manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. 33 (2000) 519 MR1832823
35 C T McMullen, The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology, Ann. Sci. École Norm. Sup. 35 (2002) 153 MR1914929
36 C T McMullen, C H Taubes, 4-manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations, Math. Res. Lett. 6 (1999) 681 MR1739225
37 C Millichap, Mutations and short geodesics in hyperbolic 3-manifolds, Comm. Anal. Geom. 25 (2017) 625 MR3702548
38 Y N Minsky, S J Taylor, Fibered faces, veering triangulations, and the arc complex, Geom. Funct. Anal. 27 (2017) 1450 MR3737367
39 H R Morton, P Traczyk, The Jones polynomial of satellite links around mutants, from: "Braids", Contemp. Math. 78, Amer. Math. Soc. (1988) 587 MR975096
40 L Mosher, Surfaces and branched surfaces transverse to pseudo-Anosov flows on 3-manifolds, J. Differential Geom. 34 (1991) 1 MR1114450
41 L Mosher, Dynamical systems and the homology norm of a 3-manifold, II, Invent. Math. 107 (1992) 243 MR1144424
42 L Mosher, Laminations and flows transverse to finite depth foliations, preprint (1996)
43 P Ozsváth, Z Szabó, Link Floer homology and the Thurston norm, J. Amer. Math. Soc. 21 (2008) 671 MR2393424
44 A Parlak, Veering triangulations and polynomial invariants of three-manifolds, PhD thesis, University of Warwick (2021)
45 A Parlak, The taut polynomial and the Alexander polynomial, J. Topol. 16 (2023) 720 MR4637975
46 A Parlak, Computation of the taut, the veering and the Teichmüller polynomials, Exp. Math. 33 (2024) 1 MR4713861
47 A Parlak, S Schleimer, H Segerman, Veering code for studying taut and veering ideal triangulations
48 D Ruberman, Mutation and volumes of knots in S3, Invent. Math. 90 (1987) 189 MR906585
49 M Shannon, Hyperbolic models for transitive topological Anosov flows in dimension three, preprint (2021) arXiv:2108.12000
50 W P Thurston, A norm for the homology of 3-manifolds, Mem. Amer. Math. Soc. 339, Amer. Math. Soc. (1986) 99 MR823443
51 C C Tsang, Veering branched surfaces, surgeries, and geodesic flows, New York J. Math. 29 (2023) 1425 MR4689115
52 C C Tsang, Veering triangulations and pseudo-Anosov flows, PhD thesis, University of California, Berkeley (2023) MR4675421
53 C C Tsang, Constructing Birkhoff sections for pseudo-Anosov flows with controlled complexity, Ergodic Theory Dynam. Systems 44 (2024) 2308 MR4798798
54 W Worden, Tnorm, Sage package, version 1.0.2 (2021)