  Thanks to a connection between two completely different topics, the classical
eigenvalue problem in a finite dimensional real vector space and the Brouwer
degree for maps between oriented differentiable real manifolds, we were able to
solve, at least in the finite dimensional context, a conjecture regarding
global continuation in nonlinear spectral theory that we formulated in some
recent papers. The infinite dimensional case seems nontrivial, and is still
unsolved.
