Bi-equivalência de aplicações bi-estáveis - Gabriel, Luiz Roberto Almeida (1979)
The main objective of this work is to set the bi-equivalence between bi-stable mappings, from the equivalences between suitable statifications of M and R2, where M is a two dimensional C∞ manifold. First we insert the concepts of bi-equivalence and bi-stability. We seek the stratifications determined by a bi-stable map f : M → R2, with f ∈ C∞ (M, R2), and we find "the stratifications mappings which accomplish the equivalence between the stratifications determined by f and g. Finally if f, g ∈ C∈ (M, R2) are bi-stable and proper mappings, and suppose the existence of a diffeomorphism k ∈ C∞ (M, R2), which induces the equivalence between the stratifications defined in R2 by f and g, we seek to show one diffeomorphism h ∈ C∞ (M,M) which accomplish together k, the bi-equivalence between f and g.