Ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces

Xin Li

*(University of Glasgow)*

9:05-10:05,August 4,2023 ÎÄ¸½Â¥ (Wenfu Building) 219

__Abstract:__

Topological groupoids describe orbit structures of dynamical systems by capturing
their local symmetries. The group of global symmetries, which are pieced together from local
ones, is called the topological full group. This construction gives rise to new examples of
groups with very interesting properties, solving outstanding open problems in group theory.
This talk is about a new connection between groupoids and topological full groups on the
one hand and algebraic K-theory spectra and infinite loop spaces on the other hand. Several
applications will be discussed. Parts of this connection already feature in work of Szymik and
Wahl on the homology of Higman-Thompson groups.

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