Fixed subgroups are compressed in surface groups

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.contributor	Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
dc.contributor.author	Zhang, Qiang
dc.contributor.author	Ventura Capell, Enric
dc.contributor.author	Wu, Jianchun
dc.date	2015-08-01
dc.identifier.citation	Zhang, Q., Ventura, E., Wu, J. Fixed subgroups are compressed in surface groups. "International journal of algebra and computation", 01 Agost 2015, vol. 25, núm. 5, p. 865-887.
dc.identifier.citation	0218-1967
dc.identifier.citation	10.1142/S0218196715500228
dc.identifier.uri	http://hdl.handle.net/2117/77518
dc.language.iso	eng
dc.relation	http://www.worldscientific.com/worldscinet/ijac
dc.relation	info:eu-repo/grantAgreement/ES/1PE/MTM2014-54896-P
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject	Group theory
dc.subject	Endomorphisms (Group theory)
dc.subject	Fixed subgroups
dc.subject	Intersections
dc.subject	Free groups
dc.subject	Surface groups
dc.subject	Direct products
dc.subject	Inertia
dc.subject	Compression
dc.subject	Hanna Neumann conjecture
dc.subject	Points
dc.subject	Bounds
dc.subject	Grups, Teoria de
dc.subject	Endomorfismes (Teoria dels grups)
dc.subject	Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups
dc.subject	Classificació AMS::57 Manifolds and cell complexes::57M Low-dimensional topology
dc.title	Fixed subgroups are compressed in surface groups
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	Electronic version of an article published as International journal of algebra and computation, Vol. 25 (5), 2015, p. 865-887 DOI: 10.1142/S0218196715500228 © [copyright World Scientific Publishing Company]
dc.description.abstract	For a compact surface Sigma (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix B, of any family B of endomorphisms of pi(1)(Sigma) is compressed in pi(1)(Sigma), i.e. rk(Fix B) <= rk(H) for any subgroup FixB <= H <= pi(1)(Sigma). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies that rk(Fix phi) <= rk(G) for every phi is an element of Aut(G).
dc.description.abstract	Peer Reviewed

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