Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Quasi-homomorphisms and stable lengths in mapping class groups

Author: D. Kotschick
Journal: Proc. Amer. Math. Soc. 132 (2004), 3167-3175
MSC (2000): Primary 20F69; Secondary 20F12, 57M07
Published electronically: May 12, 2004
MathSciNet review: 2073290
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give elementary applications of quasi-homomorphisms to growth problems in groups. A particular case concerns the number of torsion elements required to factor a given element in the mapping class group of a surface.

References [Enhancements On Off] (What's this?)

  • 1. N. A'Campo, Monodromy of real isolated singularities, Topology 42 (2003), 1229-1240. MR 2004c:14011
  • 2. C. Bavard, Longueur stable des commutateurs, Enseign. Math. 37 (1991), 109-150. MR 92g:20051
  • 3. M. Bestvina and K. Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geometry $\&$ Topology 6 (2002), 69-89. MR 2003f:57003
  • 4. V. Braungardt and D. Kotschick, Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality, Trans. Amer. Math. Soc. 355 (2003), 3217-3226. MR 2004b:57034
  • 5. T. E. Brendle and B. Farb, Every mapping class group is generated by $3$ torsion elements and by $7$ involutions, Preprint arXiv:math.GT/0307039 v2 24Jul2003.
  • 6. M. Burger and N. Monod, Bounded cohomology of lattices in higher rank Lie groups, J. Eur. Math. Soc. 1 (1999), 199-235; Erratum ibid. 1 (1999), 338. MR 2000g:57058a
  • 7. H. Endo and D. Kotschick, Bounded cohomology and non-uniform perfection of mapping class groups, Invent. Math. 144 (2001), 169-175. MR 2001m:57046
  • 8. B. Farb, A. Lubotzky and Y. N. Minsky, Rank one phenomena in mapping class groups, Duke Math. J. 106 (2001), 581-597. MR 2001k:20076
  • 9. B. Farb and H. Masur, Superrigidity and mapping class groups, Topology 37 (1998), 1169-1176. MR 99f:57017
  • 10. R. E. Gompf, A topological characterization of symplectic manifolds, arXiv:math.SG/0210103 v1 7Oct2002.
  • 11. W. J. Harvey, Branch loci in Teichmüller space, Trans. Amer. Math. Soc. 153 (1971), 387-399. MR 45:7046
  • 12. N. V. Ivanov, Mapping class groups, in Handbook of geometric topology, North-Holland, Amsterdam 2002, pp. 523-633. MR 2003h:57022
  • 13. V. A. Kaimanovich and H. Masur, The Poisson boundary of the mapping class group, Invent. Math. 125 (1996), 221-264. MR 97m:32033
  • 14. M. Korkmaz, Stable commutator length of a Dehn twist, Preprint arXiv:math.GT/0012162 v2 9Jul2003.
  • 15. M. Korkmaz, On a question of Brendle and Farb, Preprint arXiv:math.GT/0307146 v2 11Jul2003.
  • 16. D. Kotschick, On regularly fibered complex surfaces, Geometry $\&$ Topology Monographs 2: Proceedings of the Kirbyfest (1999), 291-298. MR 2001f:14020
  • 17. C. Maclachlan, Modulus space is simply connected, Proc. Amer. Math. Soc. 29 (1971), 85-86. MR 44:4202
  • 18. J. McCarthy and A. Papadopoulos, Involutions in surface mapping class groups, Enseign. Math. 33 (1987), 275-290. MR 89a:57010
  • 19. N. Monod, Continuous bounded cohomology of locally compact groups, LNM 1758, Springer Verlag 2001. MR 2002h:46121
  • 20. L. Mosher, Mapping class groups are automatic, Ann. of Math. 142 (1995), 303-384. MR 96e:57002
  • 21. L. Polterovich and Z. Rudnick, Kick stability in groups and dynamical systems, Nonlinearity 14 (2001), 1331-1363. MR 2003d:37003
  • 22. J. Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978), 347-350. MR 58:13045

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20F69, 20F12, 57M07

Retrieve articles in all journals with MSC (2000): 20F69, 20F12, 57M07

Additional Information

D. Kotschick
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, 80333 München, Germany

Received by editor(s): July 28, 2003
Published electronically: May 12, 2004
Additional Notes: The author is a member of the \sl European Differential Geometry Endeavour (EDGE), Research Training Network HPRN-CT-2000-00101, supported by The European Human Potential Programme
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society