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Daniel Allcock, : Most big mapping class groups fail the Tits Alternative
Thursday, March 04, 2021, 03:30pm - 04:30pm
A big surface S means one whose pi1 is not finitely generated. For example, S could have infinitely many punctures, or infinitely many handles, or contain a disk minus Cantor set. In any of these cases, the mapping class group of S turns out not to satisfy what is called the "Tits Alternative". (And these cases cover almost all big surfaces.)

We will give an overview of big surfaces and the Tits Alternative. This "alternative" is one of the standard properties that a group might or might not have. We will also introduce a famous group found by Grigorchuk, that plays a central role in the proof of the theorem.

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