Abstract
Let $f\colon \mathbb{G}_{n,k}\to \mathbb{G}_{m,l}$ be any continuous map between two distinct complex (resp. quaternionic) Grassmann manifolds of the same dimension. We show that the degree of $f$ is zero provided $n,m$ are sufficiently large and $l\geq 2$. 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 every element of a set of algebra generators of $H^{*}(\mathbb{G}_{m,l};\mathbb{Q})$ is determined up to a sign, $\pm$, by the degree of $f$, provided this degree is non-zero.
Citation
Parameswaran Sankaran. Swagata Sarkar. "Degrees of maps between Grassmann manifolds." Osaka J. Math. 46 (4) 1143 - 1161, December 2009.
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