Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Tits alternatives and low dimensional topology
Jonathan A. HILLMAN
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2003 Volume 55 Issue 2 Pages 365-383

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Abstract
We use cohomological group theory and properties of L2-Betti numbers to determine the solvable groups with presentations of deficiency 1, to give a new proof of the“Tits alternative”for subgroups of Haken 3-manifold groups, and to study the fundamental groups of closed 4-manifolds with Euler characteristic 0 and, in particular, 2-knot groups.
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