We show that the loop spaces on real projective spaces are topologically approximated by the spaces of rational maps RP → RP. As a byproduct of our constructions we obtain an interpretation of the… (More)

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in socalled ”quantized spaces”. Our… (More)

For X a topological space let expk X be the set of all non-empty finite subsets of X of cardinality at most k. There is a map from the Cartesian product of k copies of X with itself to expk X which… (More)

It is shown that Segal’s theorem on the spaces of rational maps from CP to CP can be extended to the spaces of continuous rational maps from CP to CP for any m 6 n. The tools are the Stone-Weierstraß… (More)

An elementary geometric construction is used to relate the space of lattices in R 2 to the space exp 3 S 1 of the subsets of a circle of cardinality at most 3. As a consequence we obtain a new proof… (More)

In this paper finite type invariants (also known as Vassiliev invariants) of pure braids are considered from a group-theoretic point of view. New results include a construction of a universal… (More)

We study the topology of the groups of real and quaternionic algebraic cycles on complcx projective spaces. By "quaternionic" cycles here we mean those invariant under the generalized antipodal map… (More)

Let us begin with definitions. Fix two points A and B in R. We shall always assume that A = (0, 0, 0) and B = (1, 0, 0) so, in particular, the line AB is the x-axis and the length of the interval… (More)

In this note we study the space of morphisms from a complex projective space to a compact smooth toric variety X. It is shown that the first author’s stability theorem for the spaces of rational maps… (More)

Dold-Thom functors are generalizations of infinite symmetric products, where integer multiplicities of points are replaced by composable elements of a partial abelian monoid. It is well-known that… (More)