Sasakian vs K-contact geometry

Juan Rojo

1 dec 2022 -- 16:15

Geometry in Como (+ online)

Here is the link to the Teams event

https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZDg2NmZkNzEtM2VmYi00NTE1LWFiMjctYjY3ZWNhMTBiYjNi%40thread.v2/0?context=%7b%22Tid%22%3a%229252ed8b-dffc-401c-86ca-6237da9991fa%22%2c%22Oid%22%3a%225276815a-fc97-4077-8301-2b30a8339375%22%7d

Abstract.

In differential geometry, a recurrent theme is to study how close the existence of a certain geometric structure on a manifold places it from the algebraic-geometry world, in a broad sense. For even dimension, the most famous instance of this problem has been the symplectic vs Kählerian question, concerning the existence of symplectic non-Kählerian manifolds. This problem has been intensively studied in the past decades, and has been an important source of development for the area known as symplectic topology. For odd dimension, an analogous problem is the K-contact vs Sasakian question, which tries to understand which manifolds (if any) admits K-contact but not Sasakian structures. In this talk we will explain a bit the analogies and differences between the two questions, and explore some of the results obtained in the past recent years for the latter, particularly in the five dimensional and simply connected case.