Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/32850
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dc.contributor.authorZimmermann, Bruno P.it
dc.date.accessioned2021-10-19T09:12:57Z-
dc.date.available2021-10-19T09:12:57Z-
dc.date.issued2021-
dc.identifier.citationBruno 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. 1-7it
dc.identifier.issn0049-4704-
dc.identifier.urihttp://hdl.handle.net/10077/32850-
dc.description.abstractWe 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.it
dc.language.isoenit
dc.publisherEUT Edizioni Università di Triesteit
dc.relation.ispartofRendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematicsit
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internazionale*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subject3-manifoldit
dc.subjectconnected sums of S² × S¹it
dc.subjectfinite group actionit
dc.subjectmapping class groupit
dc.subjectouter automorphism group of the fundamental groupit
dc.subjectNielsen realization prob-lemit
dc.titleA note on the Nielsen realization problem for connected sums of S² X S¹it
dc.typeArticleit
dc.identifier.doi10.13137/2464-8728/32850-
dc.identifier.eisbn2464-8728-
dc.subject.msc201057M60it
dc.subject.msc201057M27it
dc.subject.msc201057S25it
dc.identifier.doieutx-
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item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
item.languageiso639-1en-
item.openairetypearticle-
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)
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