  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.
