Invariants of quasi-isometries of pairs

Sam Hughes (Oxford)

Abstract: In this talk we will introduce quasi-isometries of pairs, roughly this allows us to carry a collection of subgroups through a quasi-isometry. We will discuss classical geometric properties of groups and how some of these can be upgraded to a `relative' invariant with respect to a collection of subgroups. We will then focus on relative Dehn functions and sketch a proof of their invariance under quasi-isometries of pairs. This talk is based on joint work with Eduardo Martínez-Pedroza (Memorial University of Newfoundland) and Luis Jorge Sánchez Saldaña (Universidad Nacional Autónoma de México).