Geometric and homological considerations of local crossings of n-foams

Abstract

Foams in all dimensions are defined by being modeled on a dual structure found in an [Formula: see text]-dimensional simplex. Their crossings are studied from geometric and homological points of view. A process of defining invariants thereof is outlined. Interesting research level problems are proposed. From considerations of foams, a partial order on certain families of forests is given via Hasse diagrams.