The surjectivity problem for one-generator,, one-relator extensions of torsion-free groups

Details The surjectivity problem for one-generator,, one-relator extensions of torsion-free groups The surjectivity problem for one-generator,, one-relator extensions of torsion-free groups

2000-09-10

arxiv.org/abs/math/0009101v2

Geom. Topol. 5(2001) 127-142

Mathematics

Group Theory

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper5.abs.html

Scientific paper

We use Klyachko's methods to prove that the natural map G to G-hat, where G is a torsion-free group and G-hat is obtained by adding a new generator t and a new relator w, is surjective only if w is conjugate to gt or gt^{-1} for some g in G. This solves a special case of the surjectivity problem for group extensions, raised by Cohen [Whitehead torsion, group extensions, and Zeeman's conjecture in high dimensions, Topology, 16 (1977) 79--88].

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