Degrees of maps between Grassmann manifolds
| dc.creator | Sankaran, Parameswaran | |
| dc.creator | Sarkar, Swagata | |
| dc.date | 2008-05-05 | |
| dc.date.accessioned | 2026-07-07T09:37:02Z | |
| dc.date.available | 2026-07-07T09:37:02Z | |
| dc.description | 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. | |
| dc.description | 21 pages,no figures | |
| dc.identifier | https://arxiv.org/abs/0805.0509 | |
| dc.identifier | http://arxiv.org/abs/0805.0509 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160322 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55M25 | |
| dc.title | Degrees of maps between Grassmann manifolds | |
| dc.type | text |