A note on the Nielsen realization problem for connected sums of S² X S¹
Zimmermann, Bruno P.
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.
EUT Edizioni Università di Trieste
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