Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The homotopy type of the loops on $(n-1)$-connected $(2n+1)$-manifolds   For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed
manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing
the order of the torsion subgroup in homology, the $p$-local homotopy groups of
$M$ are determined by the rank of the free Abelian part of the homology.
Moreover, we show that these $p$-local homotopy groups can be expressed as a
direct sum of $p$-local homotopy groups of spheres. The integral homotopy type
of the loop space is also computed and shown to depend only on the rank of the
free Abelian part and the torsion subgroup.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat