WHITNEY CELLULATION of WHITNEY STRATIFIED SETS and GORESKY'S HOMOLOGY CONJECTURE

C Murolo (1) , David J A Trotman (1)

1 I2M - Institut de Mathématiques de Marseille

We use the proof of Goresky of triangulation of compact abstract stratified sets and the smooth version of the Whitney fibering conjecture, together with its corollary on the existence of a local Whitney wing structure, to prove that each Whitney stratified set X = (A, Σ) admits a Whitney cellulation. We apply this result to prove the conjecture of Goresky stating that the homological representation map R : W H k (X) → H k (X) between the set of the cobordism classes of Whitney (b)-regular stratified cycles of X and the usual homology of X is a bijection. This gives a positive answer to the extension to Whitney stratified sets of the famous Thom-Steenrod representation problem of 1954.

Domaines: Topologie géométrique [math.GT]; Topologie algébrique [math.AT]; Géométrie différentielle [math.DG]

C Murolo, David J A Trotman. WHITNEY CELLULATION of WHITNEY STRATIFIED SETS and GORESKY'S HOMOLOGY CONJECTURE. 2019. ⟨hal-02014662⟩