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Parallizable manifolds and the fundamental group

Johnson, FEA; Walton, J; (2000) Parallizable manifolds and the fundamental group. Mathematika , 47 (1-2) 165 - 172. 10.1112/S0025579300015795. Green open access

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Abstract

ntroduction. 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.

Type: Article
Title: Parallizable manifolds and the fundamental group
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/S0025579300015795
Publisher version: http://dx.doi.org/10.1112/S0025579300015795
Language: English
Additional information: © 2000 Cambridge University Press
Keywords: Problems, PUBLISHED, volume, Low-dimensional topology, Geometric structures on low-dimensional manifolds
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/80990
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