BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ellen Henke (TU Dresden) DTSTART:20220425T120000Z DTEND:20220425T130000Z DTSTAMP:20260422T135903Z UID:BilTop/44 DESCRIPTION:Title: Fusion systems\, linking systems and punctured groups\nby Ellen Henke (TU Dresden) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11 .\n\nAbstract\nSaturated fusion systems and associated linking systems are categories modelling the $p$-local structure of finite groups. In particu lar\, linking systems contain the algebraic information that is needed to study $p$-completed classifying spaces of fusion systems similarly to $p$ -completed classifying spaces of finite groups. If $G$ is a finite group a nd $S$ is a Sylow $p$-subgroup of $G$\, then we can construct a saturated fusion system $\\F_S(G)$ as follows: The objects are all subgroups of $S$\ , and the morphisms between two objects are the injective group homomorphi sms induced by conjugation with elements of $G$. Saturated fusion systems which do not arise in this way are called exotic.\n\n\n\nThe concept of a linking system was generalized by Oliver and Ventura to transporter system s. Andrew Chermak introduced moreover group-like structures\, called local ities\, which correspond in a certain way to transporter systems. I will g ive an introduction to the subject and outline how the theory of localitie s can be used to prove new theorems on fusion systems. Moreover\, I will r eport on a project with Assaf Libman and Justin Lynd\, where we study "pun ctured groups''. Here a transporter system (or a locality) associated to f usion system $\\F$ over $S$ is called a punctured group if the object set is the collection of all non-identity subgroups. It should be noted in thi s context that a fusion system $\\F$ over a $p$-group $S$ can be realized as a category $\\F_S(G)$ as above if and only if there is a transporter sy stem whose object set is the full collection of subgroups of $S$. In parti cular\, to every group fusion system one can associate a punctured group. In the project with Libman and Lynd\, we determine for many of the known e xotic fusion systems whether an associated punctured group exists.\n LOCATION:https://researchseminars.org/talk/BilTop/44/ END:VEVENT END:VCALENDAR