It is shown that there does not exist a PL-bundle over S8 with fibre and total space PL-manifolds homotopy equivalent to CP and CP respectively. Consequently, the Hopf fibration over S8 admits no subfibration by PL-circles.

We describe a locally trivial quantum principal U (1)-bundle over the quantum space S 2 pq which is a noncommutative analogue of the usual Hopf bundle. We also provide results concerning the structure of its total space algebra (irreducible *-representations and topological K-groups) and its Galois aspects (Galois property, existence of a strong connection, non-cleftness).

In this note examples are presented of vector elds depending on parameters and determined by the 3{jet, which display persisent occurrence of n{quasiperiodicity. In the parameter space this occurrence has relatively large measure. A leading example consists of weakly coupled Hopf bifurcations. This example, however, is extended to full generality in the space of all 3{jets.

Let A be a simplicial bicommutative Hopf algebra over the field F2 with the property that π0A ∼= F2. We show that π∗A is a functor of the André-Quillen homology of A, where A is regarded as an F2 algebra. Then we give a method for calculating that André-Quillen homology independent of knowledge of π∗A. Let G be an abelian group. Since the work of Serre [19] and Cartan [6], we have know that the...

Let M be a k-vector space and R ∈ End k(M ⊗M). In [10] we introduced and studied what we called the Hopf equation: R12R23 = R23R13R12. By means of a FRT type theorem, we have proven that the category HM H of H-Hopf modules is deeply involved in solving this equation. In the present paper, we continue to study the Hopf equation from another perspective: having in mind the quantum Yang-Baxter equ...

We study biminimal submanifolds in contact 3-manifolds. In particular, biminimal curves in homogeneous contact Riemannian 3manifolds and biminimal Hopf cylinders in Sasakian 3-space forms are investigated. M.S.C. 2000: 53C42, 53C25.

We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W 1,2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.

In this paper, we consider a new class of generalized variational inequalities and a new class of generalized Wiener-Hopf equations involving set-valued and nonexpansive mappings in real Hilbert space. Using the projection technique, we show that the generalized variational inequalities are equivalent to the generalized Wiener-Hopf equations. Further, by using this alternative equivalence we su...

Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podleś spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf...

Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podleś spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf...