A parametrized Borsuk-Ulam theorem for Banach bundles

Neža Mramor-Kosta, Ljubljana, Slovenia

Keywords: G-index, parametrized Borsuk-Ulam theorem, Banach bundle AMS Subject classification: 55M20, 55R40, 55R25, 55N91

Abstract: The paper studies the size of the set of zeros of an equivariant map from a sphere bundle with a free action to a vector bundle with an orthogonal action of one of the groups S^{d}, d ∈ {0, 1, 3} or Z_{p}, p an odd prime. The main result is a generalization of a parametrized Borsuk-Ulam theorem, which is known for finite-dimensional bundles, to infinite-dimensional Banach bundles.