Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Up to one approximations of sectional category and topological
  complexity   James' sectional category and Farber's topological complexity are studied in
a general and unified framework.
  We introduce `relative' and `strong relative' forms of the category for a
map. We show that both can differ from sectional category just by 1. A map has
sectional or relative category less than or equal to $n$ if, and only if, it is
`dominated' (in some sense) by a map with strong relative category less than or
equal to $n$. A homotopy pushout can increase sectional category but neither
homotopy pushouts, nor homotopy pullbacks, can increase (strong) relative
category. This makes (strong) relative category a convenient tool to study
sectional category. We completely determine the sectional and relative
categories of the fibres of the Ganea fibrations.
  As a particular case, the `topological complexity' of a space is the
sectional category of the diagonal map. So it can differ from the (strong)
relative category of the diagonal just by 1. We call the strong relative
category of the diagonal `strong complexity'. We show that the strong
complexity of a suspension is at most 2.

35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat