Stiefel-Whitney classes for coherent real analytic sheaves.

Krzysztof Kurdyka (1) , Wojciech Kucharz

1 LAMA - Laboratoire de Mathématiques

The authors investigate the notion of Stiefel-Whitney classes for coherent real analytic sheaves on real analytic manifolds. These classes are characterized by their behavior on restrictions and free resolutions. They prove that the set of Stiefel-Whitney classes of coherent real analytic sheaves coincides with the set of Stiefel-Whitney classes of real analytic vector bundles. They also realize Poincaré duals to analytic subsets of codimension one or two as such Stiefel-Whitney classes. As a consequence, they prove that the subgroup of degree two Stiefel-Whitney classes of topological vector bundles coincides with the subgroup of Poincaré duals to analytic subsets of codimension two.

Mots clés: Whitney Steifel class; real analytic sheave

Domaines: Topologie géométrique [math.GT]

Krzysztof Kurdyka, Wojciech Kucharz. Stiefel-Whitney classes for coherent real analytic sheaves.. Advances in Geometry, 2007, 7 (1), pp.101-112. ⟨hal-00368868⟩