This paper is on the classical problem on isotopy classification of embeddings of manifolds into Euclidean spaces. All complete concrete classification results, except for the Haefliger classification of links and smooth knots, can be obtained using the simplest configuration spaces invariant of Haefliger-Wu. In this paper we introduce an invariant which, together with the Haefliger-Wu invarian...

Finite semifields, also known as finite non-associative division algebras, generalize finite fields. Associative semifields are (skew)fields. A slightly more general notion is a presemifield (where the existence of a multiplicative unit is no longer required). Each finite semifield has p elements for some r (p a prime). We can think of addition coinciding with the addition in the field GF (p). ...

We classify transverse Hopf links in the standard contact 3-space up to transverse isotopy in terms of their components’ self-linking number. 1 The statement of result A contact structure on a 3-manifold is a completely non-integrable 2-plane field on it. Let ξ0 be the standard contact structure on 3-space R 3 = {(x, y, z)}, that is, a 2-plane field on R defined by the kernel of the 1-form dz −...

We note an error in [2]. This Erratum will not be published. The paper defines Ham(M,ω) to be the group of Hamiltonian automorphisms, equipped with the C∞-topology, and G as “the group of smooth based loops in Ham(M,ω)”. This is a misleading formulation, since what the paper really means is that elements of G are Hamiltonian loops. If one understands it in that way, then the proof of [2, Lemma ...