The incidence correspondence and its associated maps in homotopy

TL;DR

This paper studies the incidence correspondence in Grassmannians, analyzing the induced maps on cycle spaces, which decompose into products of Eilenberg-MacLane spaces, and computes these decompositions and maps up to homotopy.

Contribution

It provides explicit homotopy decompositions of cycle spaces in Grassmannians and calculates the associated maps induced by the incidence correspondence.

Findings

Cycle spaces decompose into products of Eilenberg-MacLane spaces.

The maps induced by the incidence correspondence are computed up to homotopy.

Homotopy types of these maps are explicitly determined.

Abstract

The incidence correspondence in the grassmannian which determines the tautological bundle defines a map between cycle spaces on grassmannians. These cycle spaces decompose canonically into a product of Eilenberg-MacLane spaces. These decompositions and the associated maps are calculated up to homotopy.