The braid group of Z^n

Daan Krammer (Warwick University)

Wednesday 4th March, 2009 16:00-17:00 Mathematics Building, room 214


The braid group B of Z^n is a new group that sits somewhere between braid groups and surface mapping class groups. It is to GL(n,Z) what the braid group is to the symmetric group. I shall define B and sketch a proof that B is Garside and in particular has a solvable word problem. I describe an almost-finite presentation for B analogous to the usual presentation for the braid group. I discuss somewhat speculative similarities between B and mapping class groups. For any statement about mapping class groups, solved or unsolved, it may be interesting to try to state and prove it for B. But whether B is useful remains to be seen.

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