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Following Lin: Expansions for Groups

International Conference on Topology and Physics in Memory of Xiao-Song Lin

Nankai University, Tianjin, July 2007

Riverside, April 2000

Kyoto, September 2001

Abstract. In a beautiful 1993 paper titled Power Series Expansions and Invariants of Links, X.-S. Lin studied "expansions" for free groups, for pure braid groups and for groups of homotopy string links. Extracting from that paper, I will define an "expansion" for a group G to be (more or less) a group isomorphism from the "finite type completion" Gftc of G to its associated graded space gr Gftc. I will explain why these notions are interesting: they are related to Lie algebras and to finite type invariants. I will then discuss a number adjectives and related topics: "fibered expansions", "(quasi?) natural expansions" and "group virtualization". Don't fall asleep! There's a surprise in the last topic.

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See also Gallery: Places: Tianjin, July 2007.