Voisinages dérivés ε-barycentriques

Let Y be a finite full subcomplex of a simplicial complex X. For any subdivision X′ of X keeping Y invariant, and for ε small enough relatively to X′, we define the ε-barycentric derived neighbourhood V_ε(X′,Y) of Y in X′. Theorem: for small enoughε, and for any simplexKofY, the transverse stars ofKinV_ε(X,Y) andV_ε(X′,Y) have the same support. As a consequence, we derive at the end of the paper a decomposition theorem for p.l. homeomorphisms of a polyhedron keeping a finite subpolyhedron invariant. Keywords: Polyhedron; Simplicial complex; Derived neighbourhood; p.l. homeomorphism