Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Homotopy Type of a Poincar\'e Duality Complex after Looping   We answer a weaker version of the classification problem for the homotopy
types of $(n-2)$-connected closed orientable $(2n-1)$-manifolds. Let $n\geq 6$
be an even integer, and $X$ be a $(n-2)$-connected finite orientable Poincar\'e
$(2n-1)$-complex such that $H^{n-1}(X;\mathbb{Q})=0$ and
$H^{n-1}(X;\mathbb{Z}_2)=0$. Then its loop space homotopy type is uniquely
determined by the action of higher Bockstein operations on
$H^{n-1}(X;\mathbb{Z}_p)$ for each odd prime $p$. A stronger result is obtained
when localized at odd primes.

35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an