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Infinite periodic tree diagrams and Thompson's group F

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Sean Cleary (CCNY)

Thompson's group F is a perplexing group with a number of different ways of understanding it. F can be understood algebraically, via generators and relations with an effective normal form. F can be understood combinatorially, in terms of pairs of rooted binary trees. And F can be understood analytically, as a group of piecewise-linear homeomorphisms of an interval or as a group of maps between Cantor sets. Usually tree pair diagrams used in conjunction with F are finite, but there are some applications of infinite but periodic tree pair diagrams to understanding finite index subgroups of F and to understanding the automorphism group of F.