Monday 19th of December 2022, 14:00-15:00 in HG03.085
Andreas Schüßler
Lie algebroids and real projective blow-ups.
Lie algebroids constitute a unifying framework for various geometric structures on smooth manifolds
like the tangent bundle (actions of) Lie algebras and Poisson structures. They come with a cohomology
theory attached to them, which is an important invariant, very difficult to compute and unknown in many
cases.
In my talk I will explain the notion of Lie algebroids and their cohomology. Blowing up a sub-structure,
which essentially means replacing it with all lines transverse to it, yields a new Lie algebroid and a
map between the corresponding cohomologies. Studying this map will hopefully give more insight in Lie
algebroid cohomologies. I will thus present the construction of the real projective blow-up and discuss
smooth functions on it, giving the starting point to computing Lie algebroid cohomologies using this
technique.