How to braid a group

Resumen:

 In this talk, I will describe asymptotically rigid mapping class groups of some surfaces and explain how they can be used to construct "braided" versions of classical groups, including Thompson's and Houghton's groups. Next, I will explain how to make our asymptotically rigid mapping class groups act on contractible cube complexes with stabilisers isomorphic to finite extensions of braid groups. The rest of the talk will be dedicated to various applications of this construction, including proofs of Funar-Kapoudjian's and Degenhardt's conjectures regarding finiteness properties of braided Ptolemy-Thompson's and Houghton's groups. (Joint work with A. Lonjou and C. Urech.)

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