Dynamical n-complexes

Abstract

Abstract Using the special n -polyhedra of Matveev 2, we give a generalization to any dimension n ≥2 of the dynamical 2-complexes introduced in the author's thesis 1. We are particularly interested in codimension 1-foliations with compact leaves of these complexes. One is lead to define a particular class of homotopy equivalences between special polyhedra, which are a generalization, in high dimension, of the Whitehead moves on graphs and of the Matveev moves on special 2-polyhedra 3.