We study some algebraic properties of a class of group presentations depending on a finite number of integer parameters. This class contains many well-known groups which are interesting from a topological point of view. We find arithmetic conditions on the parameters under which the considered groups cannot be fundamental groups of hyperbolic 3-manifolds of finite volume. Then we investigate the asphericity for many presentations contained in our family.
Families of group presentations related to topology / Cavicchioli, Alberto; D., Repovs; Spaggiari, Fulvia. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 286:1(2005), pp. 41-56. [10.1016/j.jalgebra.2005.01.008]
Families of group presentations related to topology
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2005
Abstract
We study some algebraic properties of a class of group presentations depending on a finite number of integer parameters. This class contains many well-known groups which are interesting from a topological point of view. We find arithmetic conditions on the parameters under which the considered groups cannot be fundamental groups of hyperbolic 3-manifolds of finite volume. Then we investigate the asphericity for many presentations contained in our family.
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