BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joeseph MacManus (Oxford) DTSTART:20240229T140500Z DTEND:20240229T150000Z DTSTAMP:20260423T021120Z UID:GaTO/97 DESCRIPTION:Title: Gr oups quasi-isometric to planar graphs\nby Joeseph MacManus (Oxford) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nA classic and impor tant theorem\, originating in work of Mess\, states that a finitely genera ted group is quasi-isometric to a complete Riemannian plane if and only if it is a virtual surface group. Another related result obtained by Maillo t states that a finitely generated group is virtually free if and only if it is quasi-isometric to a complete planar simply connected Riemannian sur face with non-compact geodesic boundary. These results illustrate the gen eral philosophy that planarity is a very `rigid' property amongst finitely generated groups.\n\nIn this talk I will build on the above and sketch ho w to characterise those finitely generated groups which are quasi-isometri c to planar graphs. Such groups are virtually free products of free and s urface groups\, and thus virtually admit a planar Cayley graph. The main technical step is proving that such a group is accessible\, in the sense o f Dunwoody and Wall. This is achieved through a careful study of the dyna mics of quasi-actions on planar graphs.\n LOCATION:https://researchseminars.org/talk/GaTO/97/ END:VEVENT END:VCALENDAR