The Space of Linear Maps into a Grassmann Manifold

Details The Space of Linear Maps into a Grassmann Manifold The Space of Linear Maps into a Grassmann Manifold

2011-11-30

arxiv.org/abs/1111.7273v1

Mathematics

Algebraic Topology

Scientific paper

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.

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