Cat(0) and Cat (-1) dimensions of torsion free

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RECERCAT Home > Universitat Autònoma de Barcelona > Prepublicacions i preprints > View document

dc.contributor.author	Brady, Noel
dc.contributor.author	Crisp, John
dc.contributor.author	Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
dc.date	2005
dc.identifier	https://ddd.uab.cat/record/44184
dc.identifier	urn:oai:ddd.uab.cat:44184
dc.format	application/pdf
dc.language	eng
dc.publisher	Centre de Recerca Matemàtica
dc.relation	Centre de Recerca Matemàtica. Prepublicacions ;
dc.rights	open access
dc.rights	Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús
dc.rights	https://creativecommons.org/licenses/by-nc-nd/2.5/
dc.subject	Grups, Teoria dels
dc.title	Cat(0) and Cat (-1) dimensions of torsion free
dc.type	Article
dc.type	Prepublicació
dc.description.abstract	We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

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