Algebraic & Geometric Topology Volume 22, issue 1 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Nielsen equivalence in Fuchsian groups

Martin Lustig and Yoav Moriah

Algebraic & Geometric Topology 22 (2022) 189–226

DOI: 10.2140/agt.2022.22.189

Bibliography

1	H Bäärnhielm, C R Leedham-Green, The product replacement Prospector, J. Symbolic Comput. 47 (2012) 64 MR2854847
2	A F Beardon, The geometry of discrete groups, 91, Springer (1983) MR698777
3	M Boileau, H Zieschang, Heegaard genus of closed orientable Seifert 3–manifolds, Invent. Math. 76 (1984) 455 MR746538
4	M R Bridson, The strong profinite genus of a finitely presented group can be infinite, J. Eur. Math. Soc. 18 (2016) 1909 MR3531665
5	G Burde, H Zieschang, Knots, 5, de Gruyter (1985) MR808776
6	M Culler, Lifting representations to covering groups, Adv. Math. 59 (1986) 64 MR825087
7	S Dowdall, S J Taylor, Rank and Nielsen equivalence in hyperbolic extensions, Int. J. Algebra Comput. 29 (2019) 615 MR3964351
8	E R F Dutra, Nielsen equivalence in closed 2–orbifold groups, preprint (2020) arXiv:2004.09326
9	E R F Dutra, Nielsen equivalence in triangle groups, preprint (2021) arXiv:2101.05344
10	E Dutra, R Weidmann, Irreducible generating tuples of Fuchsian groups, in preparation
11	R H Fox, Free differential calculus, I : Derivation in the free group ring, Ann. of Math. 57 (1953) 547 MR53938
12	M Heusener, R Weidmann, Generating pairs of 2–bridge knot groups, Geom. Dedicata 151 (2011) 279 MR2780752
13	G Islambouli, Nielsen equivalence and trisections of 4–manifolds, preprint (2018) arXiv:1804.06978
14	I Kapovich, R Weidmann, Freely indecomposable groups acting on hyperbolic spaces, Int. J. Algebra Comput. 14 (2004) 115 MR2058318
15	I Kapovich, R Weidmann, Nielsen equivalence in a class of random groups, J. Topol. 9 (2016) 502 MR3509971
16	I Kra, On lifting Kleinian groups to SL(2, ℂ), from: "Differential geometry and complex analysis" (editors I Chavel, H M Farkas), Springer (1985) 181 MR780044
17	L Louder, Nielsen equivalence in closed surface groups, preprint (2010) arXiv:1009.0454
18	A Lubotzky, Dynamics of Aut(F_N) actions on group presentations and representations, from: "Geometry, rigidity, and group actions" (editors B Farb, D Fisher), Univ. Chicago Press (2011) 609 MR2807845
19	M Lustig, Nielsen equivalence and simple-homotopy type, Proc. Lond. Math. Soc. 62 (1991) 537 MR1095232
20	M Lustig, Y Moriah, Nielsen equivalence in Fuchsian groups and Seifert fibered spaces, Topology 30 (1991) 191 MR1098913
21	M Lustig, Y Moriah, Generating systems of groups and Reidemeister–Whitehead torsion, J. Algebra 157 (1993) 170 MR1219664
22	Y Moriah, J Schultens, Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal, Topology 37 (1998) 1089 MR1650355
23	Y Moriah, V Shpilrain, Nontame automorphisms of extensions of periodic groups, Israel J. Math. 84 (1993) 17 MR1244656
24	A Myropolska, T Nagnibeda, On transitivity and (non)amenability of AutF_n actions on group presentations, Groups Geom. Dyn. 8 (2014) 837 MR3267526
25	N Peczynski, G Rosenberger, H Zieschang, Über Erzeugende ebener diskontinuierlicher Gruppen, Invent. Math. 29 (1975) 161 MR382457
26	G Rosenberger, Zum Rang- und Isomorphieproblem für freie Produkte mit Amalgam, Habilitationsschrift, Universität Hamburg (1974)
27	G Rosenberger, Automorphismen ebener diskontinuierlicher Gruppen, from: "Riemann surfaces and related topics" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 439 MR624831
28	G Rosenberger, Minimal generating systems for plane discontinuous groups and an equation in free groups, from: "Groups" (editors A C Kim, B H Neumann), Lecture Notes in Math. 1398, Springer (1989) 170 MR1032825
29	G Rosenberger, On subgroups of free products of cyclics, from: "Proceedings of the International Conference on Algebra, I" (editors A C Kim, B H Neumann), Contemp. Math. 131, Amer. Math. Soc. (1992) 315 MR1175784
30	J Schultens, Heegaard splittings of Seifert fibered spaces with boundary, Trans. Amer. Math. Soc. 347 (1995) 2533 MR1297537
31	P Scott, The geometries of 3–manifolds, Bull. Lond. Math. Soc. 15 (1983) 401 MR705527
32	J Souto, The rank of the fundamental group of certain hyperbolic 3–manifolds fibering over the circle, from: "The Zieschang Gedenkschrift" (editors M Boileau, M Scharlemann, R Weidmann), Geom. Topol. Monogr. 14, Geom. Topol. Publ. (2008) 505 MR2484715
33	W Thurston, Geometry and topology of three-manifolds, lecture notes (1980)
34	R Weidmann, Generating tuples of free products, Bull. Lond. Math. Soc. 39 (2007) 393 MR2331566
35	A Wigderson, Interactions of computational complexity theory and mathematics, preprint (2017) arXiv:1710.09780
36	H Zieschang, Über Automorphismen ebener diskontinuierlicher Gruppen, Math. Ann. 166 (1966) 148 MR201521
37	H Zieschang, Über die Nielsensche Kürzungsmethode in freien Produkten mit Amalgam, Invent. Math. 10 (1970) 4 MR263929