Deformation retracts to intersections of Whitney stratifications

Saurabh Trivedi and David Trotman

Journal of Singularities
volume 22 (2020), 315-320

Received: 13 March 2019. Received in revised form: 28 May 2020.

DOI: 10.5427/jsing.2020.22s

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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.


Author(s) information:

Saurabh Trivedi
Indian Statistical Institute North-East Centre
Punioni Solmara, Tezpur 784501, Assam, India
and
ICMC - Universidade de São Paulo
13566-590, São Carlos, SP, Brasil

David Trotman
I2M (UMR 7353)
Centre de Mathématiques et Informatique
Aix-Marseille Université
39 rue Joliot-Curie
13453 Marseille Cedex 13, France