Fibrators help detect approximate fibrations. A closed, connected n-manifold N is called a codimension-2 fibrator if each map p : M → B defined on an (n + 2)-manifold M such that all fibre p−1(b), b ∈ B, are shape equivalent to N is an approximate fibration. The most natural objects N to study are s-Hopfian manifolds. In this note we give some necessary and sufficient conditions for s-Hopfian m...

We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n ≤ 7. Furthermore we study the case where there exists an...

Let X ⊂ P be an n-dimensional connected projective submanifold of projective space. Let p : P → P denote the projection from a linear P ⊂ P . Assuming that X 6⊂ P we have the induced rational mapping ψ := pX : X → P. This article started as an attempt to understand the structure of this mapping when ψ has a lower dimensional image. In this case of necessity we have Y := X ∩ P is nonempty. The s...

The purpose of this article is to study the Chow groups and Chow motives of the so-called wonderful compactifications of an arrangement of subvarieties, in particular the Fulton-MacPherson configuration spaces. All the varieties in the paper are over an algebraically closed field. Let Y be a nonsingular quasi-projective variety. Let S be an arrangement of subvarieties of Y (cf. Definition 2.2)....

This conjecture was proved in [9] if X is not of general type, but the general case still remains open. It was suggested in [36] that condition (a) in the case pg(X) = 0 would be related closely to the following conditions: (b) ind limUH 3 D(U,Q(2)) = 0, where U runs over nonempty open subvarieties of X . (c) The cycle map CH(U, 1)Q → H D(U,Q(2)) is surjective for any open subvarieties U of X ....

A new quaternary linear code of length 19, codimension 5, and covering radius 2 is found in a computer search using tabu search, a local search heuristic. Starting from this code, which has some useful partitioning properties, di!erent lengthening constructions are applied to get an in"nite family of new, record-breaking quaternary codes of covering radius 2 and odd codimension. An algebraic co...

A rack, which is the algebraic distillation of two of the Reidemeister moves, is a set with a binary operation such that right multiplication is an automorphism. Any codimension two link has a fundamental rack which contains more information than the fundamental group. Racks provide an elegant and complete algebraic framework in which to study links and knots in 3{manifolds, and also for the 3{...

We characterize all (n?2)-dimensional linear subspaces of Pn such that the induced projection, when restricted to rational normal curve, gives a Galois morphism. give an explicit description these spaces as disjoint union locally closed subvarieties in Grassmannian G(n?2,n).

%#(!, #, *) = %0(#) + +%1(!, #, *), * ∈ ! = R/!. We study Arnold diffusion for this system, namely, existence of orbits {(!, #)(*)}$ such that ∣#(*)− #(0)∣ > .(1) independently of +. We say that %0 has a resonance of order / < & at a point # ∈ ( if there are / linearly independent integer vectors 11, . . . , 1% ∈ Z such that 1& ⋅ ∇%0(#) = 0 for 2 = 1, ⋅ ⋅ ⋅ ,/. We say that a resonance is of co-...