Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopical stable ranks for Banach algebras   The connected stable rank and the general stable rank are homotopy invariants
for Banach algebras, whereas the Bass stable rank and the topological stable
rank should be thought of as dimensional invariants. This paper studies the two
homotopical stable ranks, viz. their general properties as well as specific
examples and computations. The picture that emerges is that of a strong
affinity between the homotopical stable ranks, and a marked contrast with the
dimensional ones.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph