Glasnik Matematicki, Vol. 42, No.1 (2007), 213-236.

QUASI-HOMOMORPHISMS ON MAPPING CLASS GROUPS

Mladen Bestvina and Koji Fujiwara

Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, Utah 84112-0090, USA
e-mail: bestvina@math.utah.edu

Graduate School of Information Science, Tohoku University, Sendai, 980-8579, Japan
e-mail: fujiwara@math.is.tohoku.ac.jp

Abstract.   We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping class group is not boundedly generated by these subgroups. In this note we enlarge the class of such subgroups. The generalization is motivated by considerations in first order theory of free groups.

2000 Mathematics Subject Classification.   57M07, 57S30.

Key words and phrases.   Mapping class group, quasi-homomorphism, bounded cohomology, pseudo-Anosov.

Full text (PDF) (free access)

DOI: 10.3336/gm.42.1.15

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