Lectures on the Euler characteristic of affine manifolds

2018/02/10 by Abad, Camilo Arias, Vásquez, Sebastián Vélez
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.03624

Abstract

These are lecture notes prepared for the summer school "Geometric, algebraic and topological methods in quantum field theory", held in Villa de Leyva in July 2017. Our goal is to provide an introduction to a conjecture of Chern that states that the Euler characteristic of a closed affine manifold vanishes. We present part of the history and motivation for the conjecture as well as some recent developments. All comments and corrections are most welcome!

Related

• Proof of Chern's conjecture on affine manifolds
• Proof of Chern conjecture for flat affine manifolds
• A roadmap to the (vanishing of the) Euler characteristic
• Invariant Measure and the Euler Characteristic of Projectively Flat Manifolds
• The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials