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Deformation Groups Satisfy an Exponential Isoperimetric Inequality

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Alexander Lowenstein (Rutgers)

Abstract: Generalizing Marc Culler and Karen Vogtmann's outer space, Max Forester, Vincent Guirardel and Gilbert Levitt came up with deformation spaces for more general group actions on simplicial metric trees. Matt Clay found an analogous barycentric spine for each of these deformation spaces. As a contractible simplicial complex acted on by the deformation group of outer automorphisms, one can ask whether or not said deformation group has an exponential Dehn function. In this talk, I will present the main ideas behind my recent work that deformation spines satisfy an exponential isoperimetric inequality. I will start with some old and new examples of deformation groups that satisfy an exponential isoperimetric inequality. I will showcase the construction of a deformation spine combinatorially and address the key concepts used to prove that they satisfy an exponential isoperimetric inequality. If time permits, I will discuss the dynamics of self foldable maps, which was an unexpected area of study necessary to complete the proof.