Journal of the Mathematical Society of Japan

Tits alternatives and low dimensional topology

Jonathan A. HILLMAN

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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.

Article information

Source
J. Math. Soc. Japan, Volume 55, Number 2 (2003), 365-383.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191419121

Digital Object Identifier
doi:10.2969/jmsj/1191419121

Mathematical Reviews number (MathSciNet)
MR1961291

Zentralblatt MATH identifier
1056.57002

Subjects
Primary: 20J05: Homological methods in group theory 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]
Secondary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}

Keywords
coherent 4-manifold $L^{2}$-Betti number minimal Seifert hypersurface Poincar\'{e} duality group solvable Tits alternative 2-knot

Citation

A. HILLMAN, Jonathan. Tits alternatives and low dimensional topology. J. Math. Soc. Japan 55 (2003), no. 2, 365--383. doi:10.2969/jmsj/1191419121. https://projecteuclid.org/euclid.jmsj/1191419121


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