In this paper we study the topology of a compactification of the space of holomorphic maps of fixed degree from ℂP1 into a finite-dimensional complex Grassmann manifold. We show that there is a homotopy equivalence through a range, increasing with the degree, between these compact spaces and an infinite-dimensional complex Grassmann manifold. These compact spaces form a direct system indexed by the degree, and the direct limit is homotopy equivalent to an infinite-dimensional complex Grassmann manifold.
All Science Journal Classification (ASJC) codes
- Geometry and Topology