zbMATH — the first resource for mathematics

Ideal Whitehead graphs in \(\mathrm{Out}(F_r)\). III: Achieved graphs in rank 3. (English) Zbl 1383.20029

20F65 Geometric group theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20E05 Free nonabelian groups
20F36 Braid groups; Artin groups
20F28 Automorphism groups of groups
57M50 General geometric structures on low-dimensional manifolds
PDF BibTeX Cite
Full Text: DOI
[1] 1. P. Arnoux et al., Fractal representation of the attractive lamination of an automorphism of the free group, Ann. Inst. Fourier56 (2006) 2161-2212. genRefLink(16, ’S1793525316500084BIB001’, ’10.5802%252Faif.2237’); · Zbl 1146.20020
[2] 2. M. Bestvina, PCMI Lectures on the geometry of Outer space, http://www.math.utah.edu/pcmi12/lecture_notes/bestvina.pdf (2012).
[3] 3. M. Bestvina, M. Feighn and M. Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal.7 (1997) 215-244. genRefLink(16, ’S1793525316500084BIB003’, ’10.1007%252FPL00001618’); · Zbl 0884.57002
[4] 4. M. Bestvina, M. Feighn and M. Handel, The Tits alternative for Out(Fn) I: Dynamics of exponentially-growing automorphisms, Ann. Math.-Second Ser.151 (2000) 517-624. genRefLink(16, ’S1793525316500084BIB004’, ’10.2307%252F121043’); · Zbl 0984.20025
[5] 5. M. Bestvina and M. Handel, Train tracks and automorphisms of free groups, Ann. Math.135 (1992) 1-51. genRefLink(16, ’S1793525316500084BIB005’, ’10.2307%252F2946562’); · Zbl 0757.57004
[6] 6. T. Coulbois and A. Hilion, Rips induction: Index of the dual lamination of an R-tree, arXiv:1002.0972.
[7] 7. T. Coulbois and A. Hilion, Botany of irreducible automorphisms of free groups, Pacific J. Math.256 (2012) 291-307. genRefLink(16, ’S1793525316500084BIB007’, ’10.2140%252Fpjm.2012.256.291’); · Zbl 1259.20031
[8] 8. T. Coulbois, A. Hilion and M. Lustig, R-trees and laminations for free groups I: Algebraic laminations, J. Lond. Math. Soc.78 (2008) 723-736. genRefLink(16, ’S1793525316500084BIB008’, ’10.1112%252Fjlms%252Fjdn052’); · Zbl 1197.20019
[9] 9. M. Culler and K. Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math.84 (1986) 91-119. genRefLink(16, ’S1793525316500084BIB009’, ’10.1007%252FBF01388734’); · Zbl 0589.20022
[10] 10. D. Cvetković and M. Petrić, A table of connected graphs on six vertices, Disc. Math.50 (1984) 37-49. genRefLink(16, ’S1793525316500084BIB010’, ’10.1016%252F0012-365X%252884%252990033-5’); · Zbl 0533.05052
[11] 11. A. Eskin, M. Mirzakhani and K. Rafi, Counting closed geodesics in strata, arXiv:1206.5574. · Zbl 1219.37006
[12] 12. B. Farb and D. Margalit, A Primer on Mapping Class Groups (pms-49) (Princeton Univ. Press, 2011). · Zbl 1245.57002
[13] 13. M. Feighn and M. Handel, The recognition theorem for Out(Fn), Groups Geom. Dyn.5 (2011) 39-106. genRefLink(16, ’S1793525316500084BIB013’, ’10.4171%252FGGD%252F116’); · Zbl 1239.20036
[14] 14. D. Gaboriau, A. Jaeger, G. Levitt and M. Lustig, An index for counting fixed points of automorphisms of free groups, Duke Math. J.93 (1998) 425-452. genRefLink(16, ’S1793525316500084BIB014’, ’10.1215%252FS0012-7094-98-09314-0’); · Zbl 0946.20010
[15] 15. D. Gaboriau and G. Levitt, The Rank of Actions on r-trees, Annales Scientifiques de l’Ecole Normale Supérieure, Vol. 28 (Société Mathématique de France, 1995), pp. 549-570. · Zbl 0835.20038
[16] 16. M. Handel and L. Mosher, Axes in Outer Space, no. 1004, Mem. Amer. Math. Soc.1004 (2011). · Zbl 1238.57002
[17] 17. A. Jäger and M. Lustig, Free group automorphisms with many fixed points at infinity, arXiv:0904.1533. · Zbl 1140.20027
[18] 18. M. Kontsevich and A. Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math.153 (2003) 631-678. genRefLink(16, ’S1793525316500084BIB018’, ’10.1007%252Fs00222-003-0303-x’); · Zbl 1087.32010
[19] 19. E. Lanneau, Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities, Comment. Math. Helvetici79 (2004) 471-501. · Zbl 1054.32007
[20] 20. E. Lanneau, Connected components of the strata of the moduli spaces of quadratic differentials, arXiv:math/0506136. · Zbl 1161.30033
[21] 21. G. Levitt and M. Lustig, Irreducible automorphisms of f_{n} have north-south dynamics on compactified outer space, J. Inst. Math. Jussieu2 (2003) 59-72. genRefLink(16, ’S1793525316500084BIB021’, ’10.1017%252FS1474748003000033’); · Zbl 1034.20038
[22] 22. J. Maher, Random walks on the mapping class group, Duke Math. J.156 (2011) 429-468. genRefLink(16, ’S1793525316500084BIB022’, ’10.1215%252F00127094-2010-216’); · Zbl 1213.37072
[23] 23. H. Masur, Interval exchange transformations and measured foliations, Ann. Math.115 (1982) 169-200. genRefLink(16, ’S1793525316500084BIB023’, ’10.2307%252F1971341’); · Zbl 0497.28012
[24] 24. H. Masur and J. Smillie, Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms, Comment. Math. Helvetici68 (1993) 289-307. genRefLink(16, ’S1793525316500084BIB024’, ’10.1007%252FBF02565820’); · Zbl 0792.30030
[25] 25. L. Mosher and C. Pfaff, Lone axes in outer space, arXiv:1311.4490. · Zbl 1388.20062
[26] 26. J. Nielsen and V. L. Hansen, Jakob Nielsen, Collected Mathematical Papers: 1913-1932, Vol. 1 (Birkhauser, 1986).
[27] 27. C. Pfaff, Constructing and classifying fully irreducible outer automorphisms of free groups, Ph.D. thesis, Rutgers University, 2012.
[28] 28. C. Pfaff, Ideal whitehead graphs in Out(Fr) I: Some unachieved graphs, To appear in New York J. Math., arXiv:1210.5762. · Zbl 1355.20036
[29] 29. C. Pfaff, Ideal Whitehead graphs in Out(Fr) II: The complete graph in each rank, J. Homotopy Relat. Struct.10 (2015) 275-301. genRefLink(16, ’S1793525316500084BIB029’, ’10.1007%252Fs40062-013-0060-5’); · Zbl 1367.20049
[30] 30. C. Pfaff, Out(F3) index realization, To appear in Math. Proc. Cambridge Philosophical Soc., arXiv:1311.4490.
[31] 31. W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. Math.115 (1982) 201-242. genRefLink(16, ’S1793525316500084BIB031’, ’10.2307%252F1971391’); · Zbl 0486.28014
[32] 32. J. H. C. Whitehead, On certain sets of elements in a free group, Proc. Lond. Math. Soc.2 (1936) 48-56. genRefLink(16, ’S1793525316500084BIB032’, ’10.1112%252Fplms%252Fs2-41.1.48’); · Zbl 0013.24801
[33] 33. A. Zorich, Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials, arXiv:1011.0395. · Zbl 1149.30033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.