Relative currents
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- by Radhika Gupta PDF
- Conform. Geom. Dyn. 21 (2017), 319-352 Request permission
Abstract:
In this paper we define currents relative to a free factor system. We prove that a fully irreducible outer automorphism relative to a free factor system acts with uniform north-south dynamics on a subspace of the space of projective relative currents.References
- Mladen Bestvina and Mark Feighn, Hyperbolicity of the complex of free factors, Adv. Math. 256 (2014), 104–155. MR 3177291, DOI 10.1016/j.aim.2014.02.001
- M. Bestvina, M. Feighn, and M. Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997), no. 2, 215–244. MR 1445386, DOI 10.1007/PL00001618
- Mladen Bestvina, Mark Feighn, and Michael Handel, The Tits alternative for $\textrm {Out}(F_n)$. I. Dynamics of exponentially-growing automorphisms, Ann. of Math. (2) 151 (2000), no. 2, 517–623. MR 1765705, DOI 10.2307/121043
- Mladen Bestvina and Michael Handel, Train tracks and automorphisms of free groups, Ann. of Math. (2) 135 (1992), no. 1, 1–51. MR 1147956, DOI 10.2307/2946562
- Francis Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988), no. 1, 139–162. MR 931208, DOI 10.1007/BF01393996
- N. Bourbaki. Éléments de mathématique. Fasc. XIII. Livre VI: Intégration. Chapitres 1, 2, 3 et 4: Inégalités de convexité, Espaces de Riesz, Mesures sur les espaces localement compacts, Prolongement d’une mesure, Espaces $L^{p}$. Deuxième édition revue et augmentée. Actualités Scientifiques et Industrielles, No. 1175. Hermann, Paris, 1965.
- P. Brinkmann, Hyperbolic automorphisms of free groups, Geom. Funct. Anal. 10 (2000), no. 5, 1071–1089. MR 1800064, DOI 10.1007/PL00001647
- Daryl Cooper, Automorphisms of free groups have finitely generated fixed point sets, J. Algebra 111 (1987), no. 2, 453–456. MR 916179, DOI 10.1016/0021-8693(87)90229-8
- Mark Feighn and Michael Handel, The recognition theorem for $\textrm {Out}(F_n)$, Groups Geom. Dyn. 5 (2011), no. 1, 39–106. MR 2763779, DOI 10.4171/GGD/116
- R. Gupta, Loxodromic elements for the relative free factor complex, arXiv:1612.04261, December 2016.
- M. Handel and L. Mosher, Subgroup decomposition in Out($F_n$): Introduction and Research Announcement, arXiv:1302.2681, February 2013.
- M. Handel and L. Mosher, Relative free splitting and relative free factor complexes I: Hyperbolicity, arXiv:1407.3508v1, 2014.
- Ilya Kapovich, The frequency space of a free group, Internat. J. Algebra Comput. 15 (2005), no. 5-6, 939–969. MR 2197815, DOI 10.1142/S0218196705002700
- Ilya Kapovich, Currents on free groups, Topological and asymptotic aspects of group theory, Contemp. Math., vol. 394, Amer. Math. Soc., Providence, RI, 2006, pp. 149–176. MR 2216713, DOI 10.1090/conm/394/07441
- Ilya Kapovich and Martin Lustig, Geometric intersection number and analogues of the curve complex for free groups, Geom. Topol. 13 (2009), no. 3, 1805–1833. MR 2496058, DOI 10.2140/gt.2009.13.1805
- M. Lustig and C. Uyanik. North-South dynamics of hyperbolic free group automorphisms on the space of currents, ArXiv e-prints, September 2015.
- Reiner Martin, Non-uniquely ergodic foliations of thin-type, measured currents and automorphisms of free groups, ProQuest LLC, Ann Arbor, MI, 1995. Thesis (Ph.D.)–University of California, Los Angeles. MR 2693216
- Howard A. Masur and Yair N. Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math. 138 (1999), no. 1, 103–149. MR 1714338, DOI 10.1007/s002220050343
- Martine Queffélec, Substitution dynamical systems—spectral analysis, Lecture Notes in Mathematics, vol. 1294, Springer-Verlag, Berlin, 1987. MR 924156, DOI 10.1007/BFb0081890
- John R. Stallings, Whitehead graphs on handlebodies, Geometric group theory down under (Canberra, 1996) de Gruyter, Berlin, 1999, pp. 317–330. MR 1714852
- Caglar Uyanik, Dynamics of hyperbolic iwips, Conform. Geom. Dyn. 18 (2014), 192–216. MR 3273532, DOI 10.1090/S1088-4173-2014-00270-7
- Caglar Uyanik, Generalized north-south dynamics on the space of geodesic currents, Geom. Dedicata 177 (2015), 129–148. MR 3370027, DOI 10.1007/s10711-014-9982-2
- J. H. C. Whitehead, On Certain Sets of Elements in a Free Group, Proc. London Math. Soc. (2) 41 (1936), no. 1, 48–56. MR 1575455, DOI 10.1112/plms/s2-41.1.48
Additional Information
- Radhika Gupta
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- Address at time of publication: Department of Mathematics, Technion, Haifa 32000, Israel
- Email: radhikagup@technion.ac.il
- Received by editor(s): February 2, 2017
- Received by editor(s) in revised form: July 8, 2017
- Published electronically: October 18, 2017
- Additional Notes: The author was partially supported by the NSF grant of Mladen Bestvina (DMS-1607236)
- © Copyright 2017 American Mathematical Society
- Journal: Conform. Geom. Dyn. 21 (2017), 319-352
- MSC (2010): Primary 20F65
- DOI: https://doi.org/10.1090/ecgd/314
- MathSciNet review: 3713836