Javier de la Nuez (University of the Basque Country): Minimality results for automorphism groups of homogeneous structures
Thursday, 12.12.2019 11:00 im Raum SR 1D
Any group G of permutations can be endowed with the so called standard
topology, the group topology in which a system of neighbourhoods of the
identity consists of the collection of all fix-point stabilizers of finite
sets and in case G is the automorphism group of a countable structure M it
is a Polish group topology. For certain classes of highly homogeneous M
such as the random graph or the dense linear order this yields interesting
examples of Polish groups with remarkable dynamical properties. Here we
take a look at the question of minimality, i.e. of whether there are no
Hausdorff group topologies on G strictly coarser than the standard
topology. We present a couple of new minimality results in case M is
the Fraïssé limit of a class with free amalgamation, as well as for
the isometry group of the Urysohn space with the point-wise convergence
topology.
(Joint work with Zaniar Ghadernezhad)
Angelegt am 05.12.2019 von Martina Pfeifer
Geändert am 05.12.2019 von Martina Pfeifer
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