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Search: MSC category 20F65 ( Geometric group theory [See also 05C25, 20E08, 57Mxx] )

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1. CJM Online first

Cohen, David Bruce
Lipschitz 1-connectedness for some solvable Lie groups
A space X is said to be Lipschitz 1-connected if every L-Lipschitz loop in X bounds a O(L)-Lipschitz disk. A Lipschitz 1-connected space admits a quadratic isoperimetric inequality, but it is unknown whether the converse is true. Cornulier and Tessera showed that certain solvable Lie groups have quadratic isoperimetric inequalities, and we extend their result to show that these groups are Lipschitz 1-connected.

Keywords:Dehn function, solvable group, lipschitz $1$-connectedness
Categories:20F65, 22E25

2. CJM 2011 (vol 64 pp. 241)

Allcock, Daniel
Triangles of Baumslag-Solitar Groups
Our main result is that many triangles of Baumslag-Solitar groups collapse to finite groups, generalizing a famous example of Hirsch and other examples due to several authors. A triangle of Baumslag-Solitar groups means a group with three generators, cyclically ordered, with each generator conjugating some power of the previous one to another power. There are six parameters, occurring in pairs, and we show that the triangle fails to be developable whenever one of the parameters divides its partner, except for a few special cases. Furthermore, under fairly general conditions, the group turns out to be finite and solvable of derived length $\leq3$. We obtain a lot of information about finite quotients, even when we cannot determine developability.

Categories:20F06, 20F65

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