Automorphism groups of finite topological rank
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- by Itay Kaplan and Pierre Simon PDF
- Trans. Amer. Math. Soc. 372 (2019), 2011-2043
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 $\omega$-categorical structure can go down to reducts. Together, those results prove that a large number of $\omega$-categorical structures that appear in the literature have an automorphism group of finite topological rank. In fact, we are not aware of any $\omega$-categorical structure to which they do not apply (assuming the automorphism group has no compact quotients). We end with a few questions and conjectures.References
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Additional Information
- Itay Kaplan
- Affiliation: Institute of Mathematics Hebrew University (The Edmond J. Safra Campus, Giv’at Ram) Jerusalem 91904, Israel
- MR Author ID: 886730
- Pierre Simon
- Affiliation: Mathematics Department, University of California, Berkeley, Evans Hall, Berkeley, California, 94720-3840
- MR Author ID: 942320
- Received by editor(s): February 6, 2018
- Received by editor(s) in revised form: July 18, 2018
- Published electronically: April 12, 2019
- Additional Notes: The first author would like to thank the Israel Science Foundation for partial support of this research (Grants no. 1533/14 and 1254/18).
The second author was partially supported by NSF (grant DMS 1665491), and the Sloan foundation. - © Copyright 2019 Itay Kaplan and Pierre Simon
- Journal: Trans. Amer. Math. Soc. 372 (2019), 2011-2043
- MSC (2010): Primary 20B27, 03C15
- DOI: https://doi.org/10.1090/tran/7674
- MathSciNet review: 3976583