Geodesic
Tits Alternative for $2$-dimensional $\mathrm {CAT}(0)$ complexes
Forum of Mathematics, Pi, Tome 10 (2022)

Voir la notice de l'article provenant de la source Cambridge University Press

We prove the Tits Alternative for groups acting on $2$-dimensional $\mathrm {CAT}(0)$ complexes with a bound on the order of the cell stabilisers. 
@article{10_1017_fmp_2022_20,
     author = {Damian Osajda and Piotr Przytycki},
     title = {Tits {Alternative} for $2$-dimensional $\mathrm {CAT}(0)$ complexes},
     journal = {Forum of Mathematics, Pi},
     publisher = {mathdoc},
     volume = {10},
     year = {2022},
     doi = {10.1017/fmp.2022.20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fmp.2022.20/}
}
TY  - JOUR
AU  - Damian Osajda
AU  - Piotr Przytycki
TI  - Tits Alternative for $2$-dimensional $\mathrm {CAT}(0)$ complexes
JO  - Forum of Mathematics, Pi
PY  - 2022
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fmp.2022.20/
DO  - 10.1017/fmp.2022.20
LA  - en
ID  - 10_1017_fmp_2022_20
ER  - 
%0 Journal Article
%A Damian Osajda
%A Piotr Przytycki
%T Tits Alternative for $2$-dimensional $\mathrm {CAT}(0)$ complexes
%J Forum of Mathematics, Pi
%D 2022
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fmp.2022.20/
%R 10.1017/fmp.2022.20
%G en
%F 10_1017_fmp_2022_20
Damian Osajda; Piotr Przytycki. Tits Alternative for $2$-dimensional $\mathrm {CAT}(0)$ complexes. Forum of Mathematics, Pi, Tome 10 (2022). doi: 10.1017/fmp.2022.20

[BB95] Ballmann, W. and Brin, M., ‘Orbihedra of nonpositive curvature’, Inst. Hautes Études Sci. Publ. Math. 82 (1995), 169–209.Google Scholar | DOI

[Bau81] Baudisch, A., ‘Subgroups of semifree groups’, Acta Math. Acad. Sci. Hungar. 38 1–4) (1981), 19–28.Google Scholar | DOI

[BB96] Ballmann, W. and Buyalo, S., ‘Nonpositively curved metrics on -polyhedra’, Math. Z. 222(1) (1996), 97–134.Google Scholar | DOI

[Bes00] Bestvina, M., Questions in geometric group theory (2000), available at https://www.math.utah.edu/bestvina/eprints/questions-updated.pdf.Google Scholar

[BF09] Bestvina, M. and Fujiwara, K., ‘A characterization of higher rank symmetric spaces via bounded cohomology’, Geom. Funct. Anal. 19(1) (2009), 11–40.Google Scholar | DOI

[Bri99] Bridson, M. R., ‘On the semisimplicity of polyhedral isometries’, Proc. Amer. Math. Soc. 127(7) (1999), 2143–2146.Google Scholar | DOI

[Bri06] Bridson, M. R., Non-positive curvature and complexity for finitely presented groups, in International Congress of Mathematicians Vol. II (European Mathematical Society, Zürich, 2006), 961–987.Google Scholar

[Bri07] Bridson, M. R., Problems concerning hyperbolic and groups (2007), available at https://docs.google.com/file/d/0B-tup63120-GVVZqNFlTcEJmMmc/edit.Google Scholar

[BH99] Bridson, M. R. and Haefliger, A., ‘Metric spaces of non-positive curvature’, in Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] vol. 319 (Springer-Verlag, Berlin, 1999), xxii+643.Google Scholar

[Can11] Cantat, S., ‘Sur les groupes de transformations birationnelles des surfaces’, Ann. of Math. (2) 174(1) (2011), 299–340 (French, with English and French summaries).Google Scholar | DOI

[Cap09] Caprace, P.-E., ‘Amenable groups and Hadamard spaces with a totally disconnected isometry group’, Comment. Math. Helv. 84(2) (2009), 437–455.Google Scholar | DOI

[Cap14] Caprace, P.-E., Lectures on proper spaces and their isometry groups, Geometric group theory’, in IAS/Park City Math. Ser. Vol. 21 (American Mathematical Society, Providence, RI, 2014), 91–125.Google Scholar

[CS11] Caprace, P.-E. and Sageev, M., ‘Rank rigidity for cube complexes’, Geom. Funct. Anal. 21(4) (2011), 851–891.Google Scholar | DOI

[CD95] Charney, R. and Davis, M. W., ‘The -problem for hyperplane complements associated to infinite reflection groups’, J. Amer. Math. Soc. 8(3) (1995), 597–627.Google Scholar

[CFS82] Cornfeld, I. P., Fomin, S. V. and Sinaĭ, Y. G., ‘ Ergodic theory ’, in Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] vol. 245 (Springer-Verlag, New York, 1982). Translated from the Russian by A. B. Sosinskiĭ.Google Scholar

[FHT11] Farb, B., Hruska, C. and Thomas, A., Problems on automorphism groups of nonpositively curved polyhedral complexes and their lattices, in Geometry, rigidity, and group actions, Chicago Lectures in Mathematics (University of Chicago Press, Chicago, IL, 2011), 515–560.Google Scholar

[GdlH90] Ghys, É. and De La Harpe, P. (eds.), ‘ Sur les groupes hyperboliques d’après Mikhael Gromov ’, in Progress in Mathematics, vol. 83 (Birkhäuser Boston, Inc., Boston, MA, 1990) xii+285 (French). Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988.Google Scholar

[Kle99] Kleiner, B., ‘The local structure of length spaces with curvature bounded above’, Math. Z. 231(3) (1999), 409–456.Google Scholar | DOI

[Lam01] Lamy, S. , ‘L’alternative de Tits pour ’, J. Algebra 239(2) (2001), 413–437. (French, with French summary).Google Scholar | DOI

[Lam22] Lamy, S., The Cremona group, Book in preparation. Preliminary version available at https://www.math.univ-toulouse.fr/%20slamy/blog/cremona.html.Google Scholar

[LP21] Lamy, S. and Przytycki, P., ‘Presqu’un immeuble pour le groupe des automorphismes modérés’, Ann. H. Lebesgue 4 (2021), 605–651.Google Scholar | DOI

[LP22] Lamy, S. and Przytycki, P., Tits Alternative for the 3-dimensional tame automorphism group, submitted, Preprint, 2022, .Google Scholar | arXiv

[Lee00] Leeb, B., A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry , in Bonner Mathematische Schriften [Bonn Mathematical Publications] vol. 326 (Universität Bonn, Mathematisches Institut, Bonn, 2000).Google Scholar

[Lyt05] Lytchak, A., ‘Rigidity of spherical buildings and joins’, Geom. Funct. Anal. 15(3) (2005), 720–752.Google Scholar | DOI

[Mar22] Martin, A., The Tits Alternative for two-dimensional Artin groups and Wise’s Power Alternative, submitted, Preprint, 2022, .Google Scholar | arXiv

[MP20] Martin, A. and Przytycki, P., ‘Tits alternative for Artin groups of type FC’, J. Group Theory 23(4) (2020), 563–573.Google Scholar | DOI

[MP21] Martin, A. and Przytycki, P., ‘Abelian subgroups of two-dimensional Artin groups’, Bull. Lond. Math. Soc. 53(5) (2021), 1338–1350.Google Scholar | DOI

[MP22] Martin, A. and Przytycki, P., ‘Acylindrical actions for two-dimensional Artin groups of hyperbolic type’, Int. Math. Res. Not. 2022(17) (2022), 13099–13127.Google Scholar | DOI

[NOP22] Norin, S., Osajda, D. and Przytycki, P., ‘Torsion groups do not act on 2-dimensional complexes’, Duke Math. J. 171(6) (2022), 1379–1415.Google Scholar | DOI

[NV02] Noskov, G. A. and Vinberg, È. B., ‘Strong Tits alternative for subgroups of Coxeter groups’, J. Lie Theory 12(1) (2002), 259–264.Google Scholar

[OP21] Osajda, D. and Przytycki, P., ‘Tits alternative for groups acting properly on 2-dimensional recurrent complexes’, Adv. Math. 391 (2021), Paper No. 107976. With an appendix by J. McCammond, D. Osajda and P. Przytycki.Google Scholar | DOI

[SW05] Sageev, M. and Wise, D. T., ‘The Tits alternative for cubical complexes’, Bull. London Math. Soc. 37(5) (2005), 706–710.Google Scholar | DOI

[Tit72] Tits, J., ‘Free subgroups in linear groups’, J. Algebra 20 (1972), 250–270.Google Scholar | DOI

[Wal82] Walters, P., An introduction to ergodic theory, Graduate Texts in Mathematics vol. 79 (Springer-Verlag, New York-Berlin, 1982).Google Scholar | DOI

Cité par Sources :