Cayley Graphs and Thompson's Group

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Infinite Groups

While the main questions about Cayley graphs of finite groups

are combinatorial, the main questions about Cayley graphs of

infinite groups are geometric.

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Alternating Groups The alternating groups are key examples of finite simple groups. One of this weekend’s speakers, Martin Kassabov, has created a family of expander graphs using Cayley graphs of Alternating groups. Below is the Cayley graph of A 4 using (123) and (12)(34) as generators. (The picture is stolen from Wolfram’s Mathworld.) 4

Infinite Groups While the main questions about Cayley graphs of finite groups are combinatorial, the main questions about Cayley graphs of infinite groups are geometric. 5

Page 1 and 2: Cayley Graphs and Thompson’s Grou
Page 3: Dihedral Groups Dihedral groups are
Page 7 and 8: Geometric Questions Many questions
Page 9 and 10: Thompson’s Group Thompson’s gro
Page 11: Strange Facts ... So F ⊕ F < F !

Cayley Graphs and Thompson's Group

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