Degrees of maps between Grassmann manifolds

Details Degrees of maps between Grassmann manifolds Degrees of maps between Grassmann manifolds

2008-05-05

arxiv.org/abs/0805.0509v1

Mathematics

Algebraic Topology

21 pages,no figures

Scientific paper

Let $f:G_{n,k}\longrightarrow G_{m,l}$ be any continuous map between any two distinct complex Grassmann manifolds of the same dimension where the target is not the complex projective space. We show that, for any given $k,l$, the degree of $f$ is zero provided that $m,n$ are sufficiently large. If the degree of $f$ is $\pm 1$, we show that $(m,l)=(n,k)$ and $f$ is a homotopy equivalence. Also, we prove that the image under $f^*$ of elements of a set of algebra generators of $H^*(G_{m,l};\mathbb{Q})$ is determined upto a sign, $\pm$, if the degree of $f$ is non-zero. Our proofs cover the case of quaternionic Grassmann manifolds as well.

Affiliated with

Also associated with

No associations

Rating

Degrees of maps between Grassmann manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Degrees of maps between Grassmann manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Degrees of maps between Grassmann manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-208784