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# Barcelona Algebraic Topology Group

Barcelona Algebraic Topology Group
 Friday's Topology Seminar 2014-2015
 Date and place: November 20, 2014. 16:00. CRM, POL-1. Speaker : Matthew Gelvin Title: Minimal characteristic bisets for saturated fusion system Abstract: A \emph{characteristic biset} for the fusion system $\mathcal{F}$ on the $p$-group $S$ is a finite set $\Omega$ with commuting left and right $S$-actions.  $\Omega$ must satisfy certain properties that mimic the left and right multiplications of $S$ on a finite Sylow supergroup inducing $\mathcal{F}$.The parameterization of $\mathcal{F}$-sets implies the existence of a unique minimal characteristic biset $\Omega_{\mathcal{F}}$, which should be thought of as \emph{the} minimal characteristic biset for $\mathcal{F}$.  In this talk, I will defend this claim by discussing the close connections between $\Omega_{\mathcal{F}}$ and other central notions in $p$-local finite group theory, including $p$-constraint, centric linking systems, and $K$-normalizers.   Date and place: November 21, 2014. 12:00. CRM, A1. Speaker : Alex González (Kansas State University) Title: Irreducible components of p-local compact groups Abstract: Irreducibility was introduced in earlier work as a criterion to classify all p-local compact groups of rank 1, and could be thought of as an algebraic analog of connectivity. A p-local compact group is said to be irreducible if its underlying fusion system contains no proper normal subsystems of maximal rank. In this talk I will sketch how to show that every p-local compact group has a unique irreducible component, by using group theoretical techniques of Chermak. Read more...

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