• Download PDF
• Download TeX
• Download bibTeX entry

Metadata

Abstract

References

[ADMQ90] Ayala, Rafael; Dominguez, Eduardo; Márquez, Adolfo C.; Quintero, Adrian Proper homotopy classification of graphs, Bull. Lond. Math. Soc., Volume 22 (1990) no. 5, pp. 417-421 | DOI | MR | Zbl

[AFV08] Armstrong, Heather; Forrest, Bradley; Vogtmann, Karen A presentation for $\mathrm{Aut}\left(F_n\right)$, J. Group Theory, Volume 11 (2008) no. 2, pp. 267-276 | DOI | MR | Zbl

[AHL + 21] Abbott, Carolyn R.; Hoganson, Hannah; Loving, Marissa; Patel, Priyam; Skipper, Rachel Finding and Combining Indicable Subgroups of Big Mapping Class Groups (2021) | arXiv | Zbl

[AKB21] Algom-Kfir, Yael; Bestvina, Mladen Groups of proper homotopy equivalences of graphs and Nielsen realization (2021) (to appear in Contemporary Mathematics) | arXiv

[All21] Allcock, Daniel Most big mapping class groups fail the Tits alternative, Algebr. Geom. Topol., Volume 21 (2021) no. 7, pp. 3675-3688 | DOI | MR | Zbl

[APV20] Aramayona, Javier; Patel, Priyam; Vlamis, Nicholas G. The first integral cohomology of pure mapping class groups, Int. Math. Res. Not., Volume 2020 (2020) no. 22, pp. 8973-8996 | DOI | MR | Zbl

[Bau63] Baumslag, Gilbert Automorphism groups of residually finite groups, J. Lond. Math. Soc., Volume 38 (1963), pp. 117-118 | DOI | MR | Zbl

[BBP23] Brendle, Tara; Broaddus, Nathan; Putman, Andrew The mapping class group of connect sums of $S^2\times S^1$, Trans. Am. Math. Soc., Volume 376 (2023) no. 4, pp. 2557-2572 | DOI | MR | Zbl

[BDR20] Bavard, Juliette; Dowdall, Spencer; Rafi, Kasra Isomorphisms between big mapping class groups, Int. Math. Res. Not., Volume 2020 (2020) no. 10, pp. 3084-3099 | DOI | MR | Zbl

[BFH00] Bestvina, Mladen; Feighn, Mark; Handel, Michael The Tits alternative for $\mathrm{Out}\left(F_n\right)$. I. Dynamics of exponentially-growing automorphisms, Ann. Math. (2), Volume 151 (2000) no. 2, pp. 517-623 | DOI | MR | Zbl

[BFH04] Bestvina, Mladen; Feighn, Mark; Handel, Michael Solvable subgroups of $\mathrm{Out}\left(F_n\right)$ are virtually Abelian, Geom. Dedicata, Volume 104 (2004), pp. 71-96 | DOI | MR | Zbl

[BFH05] Bestvina, Mladen; Feighn, Mark; Handel, Michael The Tits alternative for $\mathrm{Out}\left(F_n\right)$. II. A Kolchin type theorem, Ann. Math. (2), Volume 161 (2005) no. 1, pp. 1-59 | DOI | MR | Zbl

[BKMM12] Behrstock, Jason; Kleiner, Bruce; Minsky, Yair; Mosher, Lee Geometry and rigidity of mapping class groups, Geom. Topol., Volume 16 (2012) no. 2, pp. 781-888 | DOI | MR | Zbl

[BKP19] Baumeister, Barbara; Kielak, Dawid; Pierro, Emilio On the smallest non-abelian quotient of $\mathrm{Aut}\left(F_n\right)$, Proc. Lond. Math. Soc. (3), Volume 118 (2019) no. 6, pp. 1547-1591 | DOI | MR | Zbl

[BLM83] Birman, Joan S.; Lubotzky, Alex; McCarthy, John D. Abelian and solvable subgroups of the mapping class groups, Duke Math. J., Volume 50 (1983) no. 4, pp. 1107-1120 | DOI | MR | Zbl

[BV00] Bridson, Martin R.; Vogtmann, Karen Automorphisms of automorphism groups of free groups, J. Algebra, Volume 229 (2000) no. 2, pp. 785-792 | DOI | MR | Zbl

[Can11] Cantat, Serge Sur les groupes de transformations birationnelles des surfaces, Ann. Math. (2), Volume 174 (2011) no. 1, pp. 299-340 corrected version (2012) available from https://perso.univ-rennes1.fr/serge.cantat/Articles/cremona_long.pdf | DOI | MR | Zbl

[DHK23] Domat, George; Hoganson, Hannah; Kwak, Sanghoon Coarse geometry of pure mapping class groups of infinite graphs, Adv. Math., Volume 413 (2023), 108836 | DOI | MR | Zbl

[Din12] Dinh, Tien-Cuong Tits alternative for automorphism groups of compact Kähler manifolds, Acta Math. Vietnam., Volume 37 (2012) no. 4, pp. 513-529 | MR | Zbl

[DP20] Domat, George; Plummer, Paul First cohomology of pure mapping class groups of big genus one and zero surfaces, New York J. Math., Volume 26 (2020), pp. 322-333 | MR | Zbl

[Dud61] Dudley, R. M. Continuity of homomorphisms, Duke Math. J., Volume 28 (1961) no. 4, pp. 587-594 | DOI | MR | Zbl

[FH07] Farb, Benson; Handel, Michael Commensurations of $\mathrm{Out}\left({\mathrm{F}}_n\right)$, Publ. Math., Inst. Hautes Étud. Sci., Volume 105 (2007), pp. 1-48 | DOI | Numdam | MR | Zbl

[GP08] Grigorchuk, Rostislav; Pak, Igor Groups of intermediate growth: An introduction, Enseign. Math. (2), Volume 54 (2008) no. 3-4, pp. 251-272 | MR | Zbl

[Gri80] Grigorčuk, R. I. On Burnside’s problem on periodic groups, Funkts. Anal. Prilozh., Volume 14 (1980) no. 1, pp. 53-54 | MR | Zbl

[Gro75] Grossman, Edna K. On the residual finiteness of certain mapping class groups, J. Lond. Math. Soc. (2), Volume 9 (1974/75), pp. 160-164 | DOI | MR | Zbl

[Har86] Harer, John L. The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math., Volume 84 (1986) no. 1, pp. 157-176 | DOI | MR | Zbl

[Hat95] Hatcher, Allen Homological stability for automorphism groups of free groups, Comment. Math. Helv., Volume 70 (1995) no. 1, pp. 39-62 | DOI | MR | Zbl

[Hat02] Hatcher, Allen Algebraic Topology, Cambridge University Press, 2002 | MR | Zbl

[Hil23] Hill, Thomas Large-Scale Geometry of Pure Mapping Class Groups of Infinite-Type Surfaces (2023) | arXiv

[HMV18] Hernández, Jesús H.; Morales, Israel; Valdez, Ferrán Isomorphisms between curve graphs of infinite-type surfaces are geometric, Rocky Mt. J. Math., Volume 48 (2018) no. 6, pp. 1887-1904 | DOI | MR | Zbl

[HV98] Hatcher, Allen; Vogtmann, Karen Rational homology of $\mathrm{Aut}\left(F_n\right)$, Math. Res. Lett., Volume 5 (1998) no. 6, pp. 759-780 | DOI | MR | Zbl

[HV04] Hatcher, Allen; Vogtmann, Karen Homology stability for outer automorphism groups of free groups, Algebr. Geom. Topol., Volume 4 (2004), pp. 1253-1272 | DOI | MR | Zbl

[HW20] Horbez, Camille; Wade, Richard D. Commensurations of subgroups of $\mathrm{Out}\left(F_N\right)$, Trans. Am. Math. Soc., Volume 373 (2020) no. 4, pp. 2699-2742 | DOI | MR | Zbl

[Iva84] Ivanov, Nikolai V. Algebraic properties of the Teichmüller modular group, Dokl. Akad. Nauk SSSR, Volume 275 (1984) no. 4, pp. 786-789 | MR | Zbl

[Iva88] Ivanov, Nikolai V. Automorphisms of Teichmüller modular groups, Topology and geometry — Rohlin Seminar (Viro, Oleg Y.; Vershik, Anatoly M., eds.) (Lecture Notes in Mathematics), Volume 1346, Springer, 1988, pp. 199-270 | DOI | MR | Zbl

[Iva97] Ivanov, Nikolai V. Automorphism of complexes of curves and of Teichmüller spaces, Int. Math. Res. Not., Volume 1997 (1997) no. 14, pp. 651-666 | DOI | MR | Zbl

[Khr90] Khramtsov, D. G. Completeness of groups of outer automorphisms of free groups, Group-theoretic Investigations (Russian), Akad. Nauk SSSR Ural. Otdel., Sverdlovsk, 1990, pp. 128-143 | MR | Zbl

[Lau74] Laudenbach, François Topologie de la dimension trois: homotopie et isotopie, Astérisque, 12, Société Mathématique de France, 1974 | Numdam | MR | Zbl

[LL20] Lanier, Justin; Loving, Marissa Centers of subgroups of big mapping class groups and the Tits alternative, Glas. Mat., III. Ser., Volume 55(75) (2020) no. 1, pp. 85-91 | DOI | MR | Zbl

[Mal58] Mal’cev, Anatoly I. On homomorphisms onto finite groups, Uch. Zap. Ivanov. Gos. Pedagog Inst., Volume 18 (1958), pp. 49-60 english translation in: Translations. Series 2. American Mathematical Society, 119 (1983) 67-79. | Zbl

[McC85] McCarthy, John D. A “Tits-alternative” for subgroups of surface mapping class groups, Trans. Am. Math. Soc., Volume 291 (1985) no. 2, pp. 583-612 | DOI | MR | Zbl

[McC86] McCarthy, John D. Automorphisms of surface mapping class groups. A recent theorem of N. Ivanov, Invent. Math., Volume 84 (1986) no. 1, pp. 49-71 | DOI | MR | Zbl

[McK77] McKenzie, Ralph Automorphism groups of denumerable Boolean algebras, Can. J. Math., Volume 29 (1977) no. 3, pp. 466-471 | DOI | MR | Zbl

[Mon75] Monk, James D. On the automorphism groups of denumerable Boolean algebras, Math. Ann., Volume 216 (1975), pp. 5-10 | DOI | MR | Zbl

[MR23] Mann, Kathryn; Rafi, Kasra Large-scale geometry of big mapping class groups, Geom. Topol., Volume 27 (2023) no. 6, pp. 2237-2296 | DOI | MR | Zbl

[Nie24] Nielsen, Jakob Die Isomorphismengruppe der freien Gruppen, Math. Ann., Volume 91 (1924) no. 3-4, pp. 169-209 | DOI | MR | Zbl

[PV18] Patel, Priyam; Vlamis, Nicholas G. Algebraic and topological properties of big mapping class groups, Algebr. Geom. Topol., Volume 18 (2018) no. 7, pp. 4109-4142 | DOI | MR | Zbl

[Ros22] Rosendal, Christian Coarse geometry of topological groups, Cambridge Tracts in Mathematics, 223, Cambridge University Press, 2022 | DOI | MR | Zbl

[SC24] Schaffer-Cohen, Anschel Graphs of curves and arcs quasi-isometric to big mapping class groups, Groups Geom. Dyn., Volume 18 (2024) no. 2, pp. 705-735 | DOI | MR | Zbl

[Uda24] Udall, Brian The sphere complex of a locally finite graph (2024) | arXiv | Zbl

[Use] User83827 Is $\mathrm{Out}\left({\mathrm{F}}_{\infty }\right)$ residually finite?, Mathematics Stack Exchange https://math.stackexchange.com/q/57867 (version: 2011-08-17)