MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1295

Preprint Number 1295

Previous Next Preprint server


1295. Itay Kaplan and Pierre Simon
Automorphism groups of finite topological rank
E-mail:

Submission date: 6 September 2017

Abstract:

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group of an ω-categorical structure can go down to reducts. Together, those results prove that a large number of ω-categorical structures that appear in the literature have an automorphism group of finite topological rank. In fact, we are not aware of any ω-categorical structure to which they do not apply (assuming the automorphism group has no compact quotients). We end with a few questions and conjectures.

Mathematics Subject Classification: 20B27, 03C15

Keywords and phrases:

Full text arXiv 1709.01918: pdf, ps.


Last updated: September 8 2017 10:13 Please send your corrections to: