Cochran's βi-invariants via twisted Whitney towers

Abstract

We show that Cochran's invariants [Formula: see text] of a [Formula: see text]-component link [Formula: see text] in the [Formula: see text]-sphere can be computed as intersection invariants of certain 2-complexes in the [Formula: see text]-ball with boundary [Formula: see text]. These 2-complexes are special types of twisted Whitney towers, which we call Cochran towers, and which exhibit a new phenomenon: A Cochran tower of order [Formula: see text] allows the computation of the [Formula: see text] invariants for all [Formula: see text], i.e. simultaneous extraction of invariants from a Whitney tower at multiple orders. This is in contrast with the order [Formula: see text] Milnor invariants (requiring order [Formula: see text] Whitney towers) and consistent with Cochran's result that the [Formula: see text] are integer lifts of certain Milnor invariants.