Description
This is joint work with Mikhail Kapranov and Anton Koroshkin.
Given a smooth affine algebraic variety over the complex numbers, we prove that the Chevalley-Eilenberg cohomology of its Lie algebra of global vector fields is a topological invariant of the underlying complex manifold and is finite dimensional in every degree. The proof uses methods from factorization homology.
In this talk, we will first explain the case of smooth real manifolds as studied in the 70's (Gelfand, Fuks, Bott--Segal, Haefliger, Guillemin, ...). We will show how to transpose those methods to complex algebraic varieties.
