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      Stable commutator length in Baumslag-Solitar groups and quasimorphisms for tree actions

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          Abstract

          This paper has two parts, on Baumslag-Solitar groups and on general G-trees. In the first part we establish bounds for stable commutator length (scl) in Baumslag-Solitar groups. For a certain class of elements, we further show that scl is computable and takes rational values. We also determine exactly which of these elements admit extremal surfaces. In the second part we establish a universal lower bound of 1/12 for scl of suitable elements of any group acting on a tree. This is achieved by constructing efficient quasimorphisms. Calculations in the group BS(2,3) show that this is the best possible universal bound, thus answering a question of Calegari and Fujiwara. We also establish scl bounds for acylindrical tree actions. Returning to Baumslag-Solitar groups, we show that their scl spectra have a uniform gap: no element has scl in the interval (0, 1/12).

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          Bounded cohomology of subgroups of mapping class groups

          , (2002)
          We show that every subgroup of the mapping class group MCG(S) of a compact surface S is either virtually abelian or it has infinite dimensional second bounded cohomology. As an application, we give another proof of the Farb-Kaimanovich-Masur rigidity theorem that states that MCG(S) does not contain a higher rank lattice as a subgroup.
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            The second bounded cohomology of word-hyperbolic groups

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              The Second Bounded Cohomology of a Group Acting on a Gromov-Hyperbolic Space

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                Author and article information

                Journal
                2013-10-14
                2014-07-14
                Article
                1310.3861
                385bfce8-3296-4135-b319-005d2161e454

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                20F65 (Primary) 20E08, 20F12, 57M07 (Secondary)
                Trans. Amer. Math. Soc. 368 (2016), 4751-4785
                v2: minor changes, incorporates referee suggestions; v1: 36 pages, 10 figures
                math.GR math.GT

                Geometry & Topology,Algebra
                Geometry & Topology, Algebra

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