Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degrees of maps between Grassmann manifolds   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.

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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con