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Journal Articles Journal of Singularities Year : 2020

Deformation retracts to intersections of Whitney stratifications

Rétractes par déformation sur intersections de stratifications de Whitney

Saurabh Trivedi
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David Trotman
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Abstract

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.
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Dates and versions

hal-03186950 , version 1 (01-04-2021)

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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⟩
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