We study a notion of planar sectional curvature for polygonal complexes.<\/p>\n
These complexes are endowed with a collection of certain planar subcomplexes.<\/p>\n
The first part of the talk is devoted to a description of these objects.<\/p>\n
After that, we discuss some geometric consequences of non-positive curvature such as Gromov-hyperbolicity and positive Cheeger constant.<\/p>\n
If time permits, we draw a connection between non-positively curved geometry of the complex and the spectrum of the discrete Laplacian, the latter being defined as an operator on the faces of the complex.<\/p>\n
Joint work with Matthias Keller (Jena) and Norbert Peyerimhoff (Durham).<\/p>\n","protected":false},"excerpt":{"rendered":"
We study a notion of planar sectional curvature for polygonal complexes. These complexes are endowed with a collection of certain planar subcomplexes. The first part of the talk is devoted to a description of these objects. After that, we discuss…
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