The style of the publication list mimics the output of bibtex2html with BibTEX style amsplain.
The XHTML+MATHML format of preprints are a compactified form of what was generated by TEX4HT from LATEX sources. I highly recommend this software as it supports many LATEX constructs, packages and output formats. Its author, Eitan Gurari, is friendly, responsive and active.
I do not have the sources for some items. These are available in fewer formats with possibly lower quality.
Abstract. The stabiliser group of an automorphism group of a class 2 nilpotent group is the normal subgroup consisting of elements acting trivially on the centre of the group and on the factor gof the group by the centre. We construct torsion-free class 2 nilpotent groups whose automorphism group is the semidirect product of the stabiliser group and an arbitrary group.
Keywords: class 2 nilpotent group; automorphism group.
Abstract. Every group has a semidirect product with a locally finite p-group such that the result has an arbitrary outer automorphism group.
Keywords: outer automorphism group; locally finite p-group; Black Box.
Abstract. A generalized E-algebra is an algebra isomorphic to its own algebra of module endomorphisms. We give examples of such algebras over a Dedekind domain whose torsion part is not cyclic. It is based on earlier construction of torsion-free E-algebras.
Keywords: mixed E-rings; Dedekind domain.
Abstract. If the continuum hypothesis holds then there exists a locally finite p-group of cardinality the successor of countably infinite with trivial centre and outer automorphism group. Without any additional set theoretic hypotheses, every group is an outer automorphism group of arbitrary many locally finite p-groups.
Keywords: locally finite p-group; outer automorphism group; Black Box; Continuum Hypothesis.
Abstract. Higgins conjectured a generalization of two theorems on decomposition of subgroups of free product of groups: Kuroš Theorem and his own generalization of Grušhko's Theorem. We prove this conjecture by improving Higgins's proof of these theorems using groupoids and covers.
Keywords: free product of groups; free product of goupoids; Kuroš's theorem; Higgins's theorem; Gruško's theorem.
Abstract. The matrix type of an algebra is an equivalence relation on natural numbers. Two numbers n and m are equivalent if the ring of n × n matrices is isomorphic to the ring of m × m matrices. We prove that matrix types of ultramatricial algebras over any field is in bijection with subgroups of the multiplicative group of positive rational numbers
Keywords: matrix type of a ring; dimension group; ultramtaricial algebra; automorphism group of a dimension group.
Abstract. Let us take an arbitrary immersion with even codimension. We derive an explicit formula for the characteristic classes of its multiple point manifolds. The main trick is solving a recursion on cohomology classes using power series.
Keywords: multiple-point manifold; immersion; cobordism class; generating function.
Abstract. Solving a conjecture of Droste and Kuske, we compute the probability that a gambler will play at least a given number of rounds with a given initial wealth in the Gambler's Ruin game with a biased coin. We present several approaches to the problem.
Keywords: gambler's ruin; random linear order.
Abstract. We derive a recursion for the cohomology classes of multiple point manifolds of an arbitrary immersion with even codimension.
Keywords: multiple-point manifold; characteristic number.
Abstract. We consider Newton non-degenerate, isolated surface singularities whose link is a rational homology sphere. We provide an algorithm to compute the Newton boundary of such a singularity from its resolution graph.
Keywords: hypersurface singularities, links of singularities, resolution graphs, Newton boundary, Newton polyhedrons.
Remark. Publisher provided doi:10.1112/S0010437X07002941 does not resolve, so it is not linked.
Abstract. We provide a surgery formula for the Seiberg–Witten invariants of negative definite plumbed rational homology 3-spheres. The surgery is deleting an arbitrary vertex of the plumbing graph. The formula is additive in nature: the Seiberg–Witten invariant for a c spinorial structure is the sum of correction terms plus the Seiberg–Witten invariants for the restricted c spinorial structure of the manifolds plumbed using the components of the deleted graph. This formula was conjectured by the second author as an analogue of Okuma's additivity formula for splice-quotient singularities. As a by-product, this proves the Seiberg–Witten invariant conjecture for splice-quotient singularities.
Keywords: isolated surface singularity, plumbed 3-manifold, surgery formula for Seiberg–Witten invariants, rational homology sphere, splice-quotient singularity, Seiberg–Witten invariant conjecture.
Abstract. We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate functions. The elegant way is the language of of line bundles based on Okuma's description of the function ring of the universal abelian cover. As an easy application, we obtain a new proof of the End Curve Theorem of Neumann and Wahl.
Keywords: splice-quotient singularity, End Curve Theorem, divisorial filtration.
Abstract. Let λ be a regular cardinal. An epimorphism between abelian groups is λ-pure if it is projective with respect to abelian groups of size less than λ. We show that every cotorsion group have λ-pure projective dimension greater than 1 if and only if λ is smaller than the torsion-free part of the group. (For larger λ, the groups are λ-pure projective.) This is related to a (hard) problem of Neeman in module theory about writing modules as factors of direct sums of small modules.
Keywords: Direct sums, direct products, mixed abelian groups, cotorsion groups.
Abstract. We show that every torsion-free group representable by a finite automaton is an extension of a finite-rank free group by a direct sum of finitely many Prüfer groups. This builds on a large extent on Tsankov's proof that the group of rational numbers is not representable by a finite automaton.
Keywords: FA-presentable abelian groups, automatic structures, additive combinatorics.
Abstract. We will show that random half-integral polytopes contain certain sets with high probability, the sets of k-tuples with entries in {0, 1/2 , 1}, and exactly one entry equal to 1/2. We precisely determine the threshold number k for which the phase transition occurs. Using these random polytopes we show that establishing integer-infeasibility takes Ω(log n/ log log n) rounds of (almost) any cutting-plane procedure with high probability whenever the number of vertices is θ(3^n). As a corollary, a relationship between the number of vertices and the rank of the polytope with respect to (almost) any cutting-plane procedure follows.
Keywords: random 0-1 polytopes; cutting-plane procedure; integer infeasibility.