Geodesic
The surjectivity problem for one-generator, one-relator extensions of torsion-free groups
Cohen, Marshall M1 ; Rourke, Colin2
1 Cornell University, Ithaca, New York 14853-4102, USA
2 Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Geometry & topology, Tome 5 (2001) no. 1, pp. 127-142.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove that the natural map G →Ĝ, where G is a torsion-free group and Ĝ 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 where g ∈ G. This solves a special case of the surjectivity problem for group extensions, raised by Cohen [Topology 16 (1977) 79–88].

DOI : 10.2140/gt.2001.5.127
Keywords: surjectivity problem, torsion-free groups, Whitehead torsion, Kervaire conjecture

Cohen, Marshall M 1 ; Rourke, Colin 2

1 Cornell University, Ithaca, New York 14853-4102, USA
2 Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom 
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Cohen, Marshall M; Rourke, Colin. The surjectivity problem for one-generator, one-relator extensions of torsion-free groups. Geometry & topology, Tome 5 (2001) no. 1, pp. 127-142. doi : 10.2140/gt.2001.5.127. http://geodesic.mathdoc.fr/articles/10.2140/gt.2001.5.127/

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