Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Quasi-homomorphisms and stable lengths in mapping class groups

Author(s): D. Kotschick
Journal: Proc. Amer. Math. Soc. 132 (2004), 3167-3175.
MSC (2000): Primary 20F69; Secondary 20F12, 57M07
Posted: May 12, 2004
Retrieve article in: PDF DVI PostScript

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:

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
Email: dieter@member.ams.org

DOI: 10.1090/S0002-9939-04-07508-2
PII: S 0002-9939(04)07508-2
Received by editor(s): July 28, 2003
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google