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Parallelizable manifolds and the fundamental group

Part of:Low-dimensional topology

Published online by Cambridge University Press:  26 February 2010

F. E. A. Johnson and
J. P. Walton
F. E. A. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT.
J. P. Walton
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT.
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§0. Introduction. Low-dimensional topology is dominated by the fundamental group. However, since every finitely presented group is the fundamental group of some closed 4-manifold, it is often stated that the effective influence of π1 ends in dimension three. This is not quite true, however, and there are some interesting border disputes. In this paper, we show that, by imposing the extra condition of parallelizability on the tangent bundle, the dominion of π1 is extended by an extra dimension.

MSC classification

Secondary:57M50: Geometric structures on low-dimensional manifolds

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Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000, pp. 165 - 172
Copyright
Copyright © University College London 2000

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