If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by EX . In the present work we establish a topological classification of such bundles in terms of the first cohomology group of X with coefficients in the ring Z2.

A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular...

The phenomenon of modulation instability of continuous-wave (cw) solutions of the cubic–quintic complex Ginzburg–Landau equation is studied. It is shown that low-amplitude cw solutions are always unstable. For higher-amplitude cw solutions, there are regions of stability and regions where the cw solutions are modulationally unstable. It is found that there is an indirect relation between the st...

A countable CW complexK is quasi-finite (as defined by A.Karasev [30]) if for every finite subcomplex M of K there is a finite subcomplex e(M) containing M such that any map f : A → M , A closed in a separable metric space X satisfying XτK, there is an extension g : X → e(M) of f . Levin’s [36] results imply that none of the Eilenberg-MacLane spaces K(G, 2) is quasi-finite if G = 0. In this pap...

We prove that if a finite group G has a representation with fixity f , then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of f + 1 spheres. This shows, in particular, that every finite group acts freely and homologically trivially on some finite CW-complex homotopy equivalent to a product of spheres.

We introduce in this paper the notions of noncommutative (shortly, NC) CW-complex, noncommutative Serre fibration and show that up to homo-topy, every NC CW-complex algebra morphism is some noncommutative Serre fibration. We then deduce a six-term exact sequence for the periodic cyclic homology and for K-theory of an arbitrary noncommutative Serre fi-bration, or of a morphism in the category of...

Anders Björner characterized which finite graded partially ordered sets arise as the closure relation on cells of a finite regular CW complex. His characterization of these “CW posets” required each open interval (0̂, u) to have order complex homeomorphic to a sphere of dimension rk(u)− 2. Work of Danaraj and Klee showed that sufficient conditions were for the poset to be thin and shellable. The...