Seifert fibred knot manifolds

We consider the question of when is the closed manifold obtained by elementary surgery on an $n$-knot Seifert fibred over a 2-orbifold. After some observations on the classical case, we concentrate on the cases n=2 and 3. We have found a new family of 2-knots with torsion-free, solvable group, overlooked in earlier work. We know of no higher dimensional examples.Comment: New co-author, stronger restrictions on possible Seifert bases. Final section on 3-knots reduced to a paragraph, as a lemma was misused in the original version. Version 3; minor improvements to first paragraph and notatio

On the local-indicability cohen–lyndon theorem

For a group H and a subset X of H, we let HX denote the set {hxh?1 | h ? H, x ? X}, and when X is a free-generating set of H, we say that the set HX is a Whitehead subset of H. For a group F and an element r of F, we say that r is Cohen–Lyndon aspherical in F if F{r} is a Whitehead subset of the subgroup of F that is generated by F{r}. In 1963, Cohen and Lyndon (D. E. Cohen and R. C. Lyndon, Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc. 108 (1963), 526–537) independently showed that in each free group each non-trivial element is Cohen–Lyndon aspherical. Their proof used the celebrated induction method devised by Magnus in 1930 to study one-relator groups. In 1987, Edjvet and Howie (M. Edjvet and J. Howie, A Cohen–Lyndon theorem for free products of locally indicable groups, J. Pure Appl. Algebra 45 (1987), 41–44) showed that if A and B are locally indicable groups, then each cyclically reduced element of A*B that does not lie in A ? B is Cohen–Lyndon aspherical in A*B. Their proof used the original Cohen–Lyndon theorem. Using Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem, one can deduce the local-indicability Cohen–Lyndon theorem: if F is a locally indicable group and T is an F-tree with trivial edge stabilisers, then each element of F that fixes no vertex of T is Cohen–Lyndon aspherical in F. Conversely, by Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem are immediate consequences of the local-indicability Cohen–Lyndon theorem. In this paper we give a detailed review of a Bass–Serre theoretical form of Howie induction and arrange the arguments of Edjvet and Howie into a Howie-inductive proof of the local-indicability Cohen–Lyndon theorem that uses neither Magnus induction nor the original Cohen–Lyndon theorem. We conclude with a review of some standard applications of Cohen–Lyndon asphericit

Finite complete rewriting systems for regular semigroups

It is proved that, given a (von Neumann) regular semigroup with finitely many left and right ideals, if every maximal subgroup is presentable by a finite complete rewriting system, then so is the semigroup. To achieve this, the following two results are proved: the property of being defined by a finite complete rewriting system is preserved when taking an ideal extension by a semigroup defined by a finite complete rewriting system; a completely 0-simple semigroup with finitely many left and right ideals admits a presentation by a finite complete rewriting system provided all of its maximal subgroups do.Comment: 11 page

Mapping the potential within a nanoscale undoped GaAs region using a scanning electron microscope

Semiconductor dopant profiling using secondary electron imaging in a scanning electron microscope (SEM) has been developed in recent years. In this paper, we show that the mechanism behind it also allows mapping of the electric potential of undoped regions. By using an unbiased GaAs/AlGaAs heterostructure, this article demonstrates the direct observation of the electrostatic potential variation inside a 90nm wide undoped GaAs channel surrounded by ionized dopants. The secondary electron emission intensities are compared with two-dimensional numerical solutions of the electric potential.Comment: 7 pages, 3 figure

Young's experiment and the finiteness of information

Young's experiment is the quintessential quantum experiment. It is argued here that quantum interference is a consequence of the finiteness of information. The observer has the choice whether that information manifests itself as path information or in the interference pattern or in both partially to the extent defined by the finiteness of information.Comment: 5 pages, 3 figures, typos remove

One Relator Quotients of Graph Products

In this paper, we generalise Magnus' Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable polycyclic groups

The structure of one-relator relative presentations and their centres

Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\} such that the word w' obtained from w by erasing all letters belonging to G is not a proper power in the free group F(x_1,...,x_n). We show how to reduce the study of the relative presentation \^G= to the case n=1. It turns out that an "n-variable" group \^G can be constructed from similar "one-variable" groups using an explicit construction similar to wreath product. As an illustration, we prove that, for n>1, the centre of \^G is always trivial. For n=1, the centre of \^G is also almost always trivial; there are several exceptions, and all of them are known.Comment: 15 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V4: the intoduction is rewritten; Section 1 is extended; a short introduction to Secton 5 is added; some misprints are corrected and some cosmetic improvements are mad

Arterial occlusion: a radiological study of a series of patients with peripheral, arterial disease

An unselected series of 546 patients, on whom 946 arteriograms were performed is considered.1250 complete arterial occlusions were found. The incidence was 2.3 per patient, both in men and in women.It is suggested that the sex distribution of peripheral vascular disease in a population is more accurately indicated by the findings in gangrene and pregangrene where there are 2.3 and 2 men, respectively to 1 woman, than by those in intermittent claudication where the sex ratio is 4.8 men to 1 woman,Aortographic evidence is presented to suggest that aortic occlusion may originate directly in the aorta itself, in women, more commonly than previously believed.On the symptomatic side occlusion in the femoro -popliteal segment alone occurs in only 43.5% of the occluded symptomatic limbs in men, and in only 34.6% of those in women.Femoro-popliteal occlusion with leg artery occlusion occurs in 43.2% of the occluded symptomatic limbs in men, and in 40.7% of those in women.Leg artery occlusion alone occurs in 13.3% of the occluded symptomatic limbs in men, and in 24.7% of those in women.On the asymptomatic side femoro-popliteal artery occlusion alone occurs in 19.8% of the occluded limbs of men and in 9.7% in women. Femoro -popliteal occlusions with associated leg artery occlusion occurs in 20.7% of the occluded asymptomatic limbs in men, and in 25.8% of those in women. Leg artery occlusion alone occurs in 59.5% of the occluded asymptomatic limbs in men and in 64.5% of those in women.The patterns of occlusion in the lower limbs are recorded. The commonest pattern is occlusion of the superficial femoral artery alone, in both women and men. Second most common is occlusion of the anterior tibial artery alone in men, and of the posterior tibial artery alone in women,The occlusion patterns in men and women are considered in intermittent claudication, gangrene and pregangrene.Patients with complete occlusion in the aortoiliac group are younger than those with complete occlusion in the femoro-popliteal group.The patients with complete occlusion in the femoro-popliteal group are older than those without complete occlusion. In the aortoiliac group those with complete occlusion are younger than those without,The incidence of leg artery occlusion is the same in the symptomatic and asymptomatic limbs in intermittent claudication.It is suggested that there is evidence that the first artery to show complete occlusion in the lower limb tends to be a leg artery.The incidence of complete occlusion is higher in limbs in patients with unilateral symptoms, than in those with bilateral symptoms.The peak incidence of occlusion in the femoro-popliteal segment in women is more proximal in the adductor canal than in men.The femoro-popliteal occlusions in the limbs with leg artery occlusion are longer than in those without, and show a greater tendency to popliteal artery involvement.The occlusions in the symptomatic and asymptomatic limbs are considered. They are, very broadly, similar in their histographic appearances