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Original scientific paper
https://doi.org/10.3336/gm.55.2.09

The minimally displaced set of an irreducible automorphism is locally finite

Stefano Francaviglia   ORCID icon orcid.org/0000-0001-5732-3191 ; Dipartimento di Matematica, University of Bologna, Italy
Armando Martino ; Mathematical Sciences, University of Southampton, United Kingdom
Dionysios Syrigos ; Mathematical Sciences, University of Southampton, United Kingdom

Fulltext: english, pdf (309 KB) pages 301-336 downloads: 58* cite
APA 6th Edition
Francaviglia, S., Martino, A. & Syrigos, D. (2020). The minimally displaced set of an irreducible automorphism is locally finite. Glasnik matematički, 55 (2), 301-336. https://doi.org/10.3336/gm.55.2.09
MLA 8th Edition
Francaviglia, Stefano, et al. "The minimally displaced set of an irreducible automorphism is locally finite." Glasnik matematički, vol. 55, no. 2, 2020, pp. 301-336. https://doi.org/10.3336/gm.55.2.09. Accessed 26 Oct. 2021.
Chicago 17th Edition
Francaviglia, Stefano, Armando Martino and Dionysios Syrigos. "The minimally displaced set of an irreducible automorphism is locally finite." Glasnik matematički 55, no. 2 (2020): 301-336. https://doi.org/10.3336/gm.55.2.09
Harvard
Francaviglia, S., Martino, A., and Syrigos, D. (2020). 'The minimally displaced set of an irreducible automorphism is locally finite', Glasnik matematički, 55(2), pp. 301-336. https://doi.org/10.3336/gm.55.2.09
Vancouver
Francaviglia S, Martino A, Syrigos D. The minimally displaced set of an irreducible automorphism is locally finite. Glasnik matematički [Internet]. 2020 [cited 2021 October 26];55(2):301-336. https://doi.org/10.3336/gm.55.2.09
IEEE
S. Francaviglia, A. Martino and D. Syrigos, "The minimally displaced set of an irreducible automorphism is locally finite", Glasnik matematički, vol.55, no. 2, pp. 301-336, 2020. [Online]. https://doi.org/10.3336/gm.55.2.09

Abstracts
We prove that the minimally displaced set of a relatively irreducible automorphism of a free splitting, situated in a deformation space, is uniformly locally finite. The minimally displaced set coincides with the train track points for an irreducible automorphism. We develop the theory in a general setting of deformation spaces of free products, having in mind the study of the action of reducible automorphisms of a free group on the simplicial bordification of Outer Space. For instance, a reducible automorphism will have invariant free factors, act on the corresponding stratum of the bordification, and in that deformation space it may be irreducible (sometimes this is referred as relative irreducibility).

Keywords
Relative outer space; min set; automorphims of free products of groups; irreducible automorphisms

Hrčak ID: 248669

URI
https://hrcak.srce.hr/248669

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