Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conley pairs in geometry - Lusternik-Schnirelmann theory and more   Firstly, we wish to motivate that Conley pairs, realized via Salamon's
definition [17], are rather useful building blocks in geometry: Initially we
met Conley pairs in an attempt to construct Morse filtrations of free loop
spaces [21]. From this fell off quite naturally, firstly, an alternative proof
[20] of the cell attachment theorem in Morse theory [13] and, secondly, some
ideas [12] how to try to organize the closures of the unstable manifolds of a
Morse-Smale gradient flow as a CW decomposition of the underlying manifold.
Relaxing non-degeneracy of critical points to isolatedness we use these Conley
pairs to implement the gradient flow proof of the Lusternik-Schnirelmann
Theorem [10] proposed in Bott's survey [3].
  Secondly, we shall use this opportunity to provide an exposition of
Lusternik-Schnirelmann (LS) theory based on thickenings of unstable manifolds
via Conley pairs. We shall cover the Lusternik-Schnirelmann Theorem [10],
cuplength, subordination, the LS refined minimax principle, and a variant of
the LS category called ambient category.

3
The categories of this paper are: physics
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat