Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifolds which admit maps with finitely many critical points into
  spheres of small dimensions   We construct, for $m\geq 6$ and $2n\leq m$, closed manifolds $M^{m}$ with
finite nonzero $\varphi(M^{m},S^{n}$), where $\varphi(M,N)$ denotes the minimum
number of critical points of a smooth map $M\to N$. We also give some explicit
families of examples for even $m\geq 6, n=3$, taking advantage of the Lie group
structure on $S^3$. Moreover, there are infinitely many such examples with
$\varphi(M^{m},S^{n})=1$. Eventually we compute the signature of the manifolds
$M^{2n}$ occurring for even $n$.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas