Foliated and compactly supported isotopies of regular neighbourhoods

Sergiy Maksymenko
Institute of Mathematics of the National Academy of Sciences of Ukraine

Date(s) : 22/09/2022   iCal
11 h 00 min - 12 h 00 min

Exposé sur Zoom avec transmission live dans la salle des séminaires.

Let F be a foliation with a “singular” submanifold B on a smooth manifold M and E be a regular neighbourhood of B in M.
Under certain “homogeneity” assumptions on F near B it is proved that every leaf preserving diffeomorphism h of M is isotopic via a leaf preserving isotopy to a diffeomorphism which coincides with some vector bundle morphism of E near B. This result is mutually a foliated and compactly supported variant of a well known statement that every diffeomorphism h of Rn fixing the origin is isotopic to the linear isomorphism induced by its Jacobi matrix of h at 0.

I also present examples of computation of the homotopy type of the group of leaf preserving diffeomorphisms of certain simple Morse-Bott foliations on lens spaces.

The talk is based on the recent preprint
with Oleksandra Khokhliuk

Coordonnées réunion Zoom:

Sujet : Séminaire de Géométrie et Topologie de Marseille
Heure : 22 sept. 2022 10:30 AM Paris

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ID de réunion : 884 8659 1060
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FRUMAM, St Charles (2ème étage)


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