Biblioteca de la Universidad Complutense de Madrid

Quasiaspherical knots with infinitely many ends


Montesinos Amilibia, José María y González Acuña, Francisco Javier (1983) Quasiaspherical knots with infinitely many ends. Commentarii Mathematici Helvetici , 58 (2). pp. 257-263. ISSN 0010-2571

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.


URL Oficial:


A smooth n-knot K in Sn+2 is said to be quasiaspherical if Hn+1(U)=0, where U is the universal cover of the exterior of K. Let G be the group of K and H the subgroup generated by a meridian. Then (G,H) is said to be unsplittable if G does not have a free product with amalgamation decomposition A∗FB with F finite and H contained in A. The authors prove that K is quasiaspherical if and only if (G,H) is unsplittable. If the group of K has a finite number of ends, then K is quasiaspherical and it was conjectured by the reviewer [J. Pure Appl. Algebra 20 (1981), no. 3, 317–324; MR0604323 (82j:57019)] that the converse was true. The authors give a very nice and useful method of constructing knots in Sn+2 and apply this method to produce counterexamples to the conjecture.

Tipo de documento:Artículo
Palabras clave:quasiaspherical n-knot; knot group; free product with amalgamation over a finite group; HNN-extension over a finite subgroup; infinitely many ends
Materias:Ciencias > Matemáticas > Topología
Código ID:17190

BIERI, R.,Mayer-Vietoris sequences for HNN-groups and homological duality, Math. Z.143 (1975) 123–130.

GONZÁLEZ-ACUÑA, F., andMONTESINOS, J. M.,Ends of knot groups, Annals of Math.108 (1978) 91–96.

LOMONACO, S.,The homotopy groups of knots I; how to compute the algebraic 2-type, Pacific J. Math.95 (1981) 349–390.

RATCLIFFE, J.,On the ends of higher dimensional knot groups, J. Pure and Appl. Alg.20 (1981) 317–324

STALLINGS, J.,Group theory and three-dimensional manifolds, New Haven and London, Yale University Press (1971).

SWAN, R. G.,Groups of cohomological dimension one, Journal of Algebra12 (1969) 585–601.

SWARUP, A.,An unknotting criterion, Journal of Pure and Applied Algebra6 (1975) 291–296.

WALL, C. T. C.,Pairs of relative cohomological dimension one, Journal of Pure and Applied Algebra1 (1971) 141–154.

SERRE, J. P. Arbres, Amalgames, Sl 2, Asterisque46 (1977).

DUNWOODY, M. J.,Accessibility and groups of cohomological dimension one, Proc. London Math. Soc.38 (1979), 193–215.

Depositado:23 Nov 2012 11:59
Última Modificación:23 Nov 2012 11:59

Sólo personal del repositorio: página de control del artículo