Proof of Chern conjecture for flat affine manifolds
Mihail Cocos
TL;DR
This paper proves the Chern conjecture for closed flat affine manifolds, demonstrating that their Euler characteristic is zero, using a novel deformation approach for the Euler form.
Contribution
It introduces a new deformation argument for the Euler form to prove the Chern conjecture in the context of flat affine manifolds.
Findings
Euler characteristic vanishes for closed flat affine manifolds
Deformation argument for the Euler form is effective
Chern conjecture is proven in this setting
Abstract
We prove Chern conjecture, which states that the Euler characteristic vanishes for closed flat affine manifolds. Our key innovation is a deformation argument for the Euler form.
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Taxonomy
TopicsGeometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows