The Space of Linear Maps into a Grassmann Manifold
Algebraic Topology
2011-12-01 v1 Algebraic Geometry
Abstract
We show that the space of all holomorphic maps of degree one from the Riemann sphere into a Grassmann manifold is a sphere bundle over a flag manifold. Using the notions of "kernel" and "span" of a map, we completely identify the space of unparameterized maps as well. The illustrative case of maps into the quadric Grassmann manifold is discussed in details and the homology of the corresponding spaces computed.
Keywords
Cite
@article{arxiv.1111.7273,
title = {The Space of Linear Maps into a Grassmann Manifold},
author = {Sadok Kallel and Paolo Salvatore and Walid Ben Hammouda},
journal= {arXiv preprint arXiv:1111.7273},
year = {2011}
}