题目: Intersections Norms and Birkhoff Sections

报告人: Pierre Dehornoy (Université Grenoble Alpes, associate professor)

时间: 2016年5月17日14:30-16:30

地点: 致远楼108室

摘要: For every finite collection of closed curves on a surface, we introduce an associated norm on the homology of this surface. These norms are reminiscent of Thurston's norm on the homology of a 3-manifold and share many of its properties, but they are more elementary. In particular, the unit ball of the dual norm on the cohomology is the convex hull of finitely many explicit points. We give an interpretation of these points in terms of certain coorientations of the original curves. All of this is then used in order to classify up to isotopy surfaces with prescribed boundary in the unit tangent bundle that are transverse to the geodesic flow.

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