Speaker: Benjamin Hennion (University Paris Sud (Paris 11 -- Orsay))
Title: Gelfand-Fuks cohomology and factorization homology
Abstract: (this is joint work with M. Kapranov)
Given a smooth affine algebraic variety over the complex numbers, we compute the Chevalley-Eilenberg cohomology of its Lie algebra of global vector fields, we show it is a topological invariant of the underlying complex manifold and is finite dimensional in every degree. The proof uses methods from factorization homology in both topological and algebraic flavors.
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 then show how to transpose those methods to complex algebraic varieties.