Tits alternatives for groups of small cohomological dimension


Jonathan A. Hillman


Research Report 96-39
Date: 28 November 1996


A well-known theorem of Tits asserts that every finitely generated linear group is either virtually solvable or contains a nonabelian free subgroup. In this note we shall show that similar "Tits alternatives" hold for groups of cohomological dimension two, 3-dimensional Poincaré duality groups and 2-knot groups. (Our arguments require some additional hypotheses.) We also give several equivalent characterizations of coherent elementary amenable 2-knot groups, and determine the deficiencies of such groups in most cases.

Key phrases

coherent. deficiency. 4-manifold. L2-Betti number. minimal Seifert hypersurface. Poincaré duality group. Tits alternative.

AMS Subject Classification (1991)

Primary: 57Q45
Secondary: 20J05, 57N13


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