RT Journal Article
T1 Quasiaspherical knots with infinitely many ends
A1 Montesinos Amilibia, José María
A1 González Acuña, Francisco Javier
AB 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.
PB European Mathematical Society
SN 0010-2571
YR 1983
FD 1983
LK https://hdl.handle.net/20.500.14352/64700
UL https://hdl.handle.net/20.500.14352/64700
LA eng
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NO Comission Asesora del MUI
DS Docta Complutense
RD 1 may 2024