Event

Talk
Chern's conjecture for special affine manifolds
Bruno Klingler (Jussieu)
8 Dec 2016, 15:30 – 16:30

An affine manifold X is a manifold admitting an atlas of charts with value in an affine space V with locally constant change of coordinates in the affine group Aff(V) of V. Equivalently, it is a manifold admitting a flat torsion free connection on its tangent bundle. Around 1955 Chern asked if there is any topological obstruction to the existence of an affine structure on a compact manifold X. He conjectured that the Euler characteristic e(TX) of any compact affine manifold has to vanish. I will discuss this conjecture and a proof when X is special affine (i.e. X is affine and moreover admits a parallel volume form).