Deformation retracts to intersections of Whitney stratifications

Rétractes par déformation sur intersections de stratifications de Whitney

Saurabh Trivedi , David Trotman (1)

1 I2M - Institut de Mathématiques de Marseille

We give a counterexample to a conjecture of Eyral on the existence of deformation retracts to intersections of Whitney stratifications embedded in a smooth manifold. We then prove that the conjecture holds if the stratifications are definable in some o-minimal structure without assuming any regularity conditions. Moreover, we also show that the conjecture holds for Whitney stratifications if they intersect transversally.

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

Saurabh Trivedi, David Trotman. Deformation retracts to intersections of Whitney stratifications. Journal of Singularities, 2020, 22, pp.315-320. ⟨10.5427/jsing.2020.22s⟩. ⟨hal-03186950⟩