Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/32850
Title: A note on the Nielsen realization problem for connected sums of S² X S¹
Authors: Zimmermann, Bruno P.
Keywords: 3-manifoldconnected sums of S² × S¹finite group actionmapping class groupouter automorphism group of the fundamental groupNielsen realization prob-lem
Issue Date: 2021
Publisher: EUT Edizioni Università di Trieste
Source: Bruno P. Zimmermann, "A note on the Nielsen realization problem for connected sums of S² X S¹" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)", EUT Edizioni Università di Trieste, Trieste, 2021. pp. 1-7
Journal: Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
We consider finite group-actions on 3-manifolds Hg obtained as the connected sum of g copies of S² × S¹, with free funda-
mental group Fg of rank g. We prove that, for g > 1, a finite group of diffeomorphisms of Hg inducing a trivial action on homology is cyclic and embeds into an S¹-action on Hg. As a consequence, no nontrivial element of the twist subgroup of the mapping class group of Hg (gen-erated by Dehn twists along embedded 2-spheres) can be realized by a
periodic diffeomorphism of Hg (in the sense of the Nielsen realization problem). We also discuss when a finite subgroup of the outer automor-
phism group Out(Fg) of the fundamental group of Hg can be realized by a group of diffeomorphisms of Hg.
Type: Article
URI: http://hdl.handle.net/10077/32850
ISSN: 0049-4704
eISBN: 2464-8728
DOI: 10.13137/2464-8728/32850
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)

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