Relative phantom maps and rational homotopy

Rational homotopy stability for the spaces of rational maps

Let Holnx0(CP 1,X) be the space of based holomorphic maps of degree n from CP1 into a simply connected algebraic variety X. Under some condition we prove that the map Holnx0(CP 1,X) −→ Hol x0 (CP 1,X) obtained by compositing f ∈ Holnx0(CP 1,X) with g(z) = z, z ∈ CP1 induces rational homotopy equivalence up to some dimension, which tends to infinity as the degree grows.

Homotopy of Rational Maps and the Quantization of Skyrmions

The Skyrme model is a classical field theory which models the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein-Rubinstein constraints into account. The aim of this paper is to show how to calculate these FR constraints directly from the rational ...

Phantom Maps and Chromatic Phantom Maps

In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or nothing behaviour is preserved when X is replaced with V ∧ X for V finite. In the second part, we introduce chromatic phantom maps. A map is n-phantom if it is null when restricted to finite spectra of type...

Se p 20 03 CYCLIC MAPS IN RATIONAL HOMOTOPY THEORY

The notion of a cyclic map g : A→ X is a natural generalization of a Gottlieb element in πn(X). We investigate cyclic maps from a rational homotopy theory point of view. We show a number of results for rationalized cyclic maps which generalize well-known results on the rationalized Gottlieb

Relative Compactness and Product Stable Quotient Maps