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A note on the Nielsen realization problem for connected sums of S² X S¹
Zimmermann, Bruno P.
2021
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e-ISBN
2464-8728
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.
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
Languages
en
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