SYGN 2012 Abstracts - Norbert Seifter

Various aspects of vertex-transitive graphs with polynomial growth
Norbert Seifter (Montanuniversität Leoben, Austria)

Following M. Gromov’s characterization of finitely generated groups with polynomial growth, V. I. Trofimov proved that the automorphism groups of locally finite vertex-transitive graphs with polynomial growth are closely related to finitely generated groups with polynomial growth. Trofimov’s characterization opened a wide field of research and led to several nice results; among others to a recently developed asymptotic invariant of vertex-transitive graphs with polynomial growth which describes the large-scale geometry of these graphs.