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

Groups of Fibonacci type revisited

This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway?s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repov?s, they have enjoyed renewed interest in recent years. We survey results concerning their algebraic properties, such as isomorphisms within the class, the classification of the finite groups, small cancellation properties, abelianizations, asphericity, connections with Labelled Oriented Graph groups, and the semigroups of Fibonacci type. Further, we present a new method of proving the classification of the finite groups that deals with all but three groups