A combinatorial Chern-Weil theorem for 2-plane bundles with even Euler characteristics
type: Item
instance of: scholarly article
title: A combinatorial Chern-Weil theorem for 2-plane bundles with even Euler characteristics
zbMATH Open document ID: 0723.57018
DOI: 10.1007/BF02937295
author: Ethan D. Bloch
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The main result gives a formula \(\chi (\xi)=C(\xi)\) for a 2-plane bundle \(\xi\) over a surface where \(\chi\) (\(\xi\)) is the Euler class (which is assumed to be even) and C(\(\xi\)) is a combinatorial Chern-Weil class, the latter being defined in terms of triangulations, normal vectors and classifying maps for \(\xi\). The curvature of polyhedral surfaces is expressed by exterior angles, the combinatorial Gauss map, and by areas of spherical geodesic triangles.
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 4192669
zbMATH Keywords: 2-plane bundle
zbMATH Keywords: surface
zbMATH Keywords: Euler class
zbMATH Keywords: combinatorial Chern-Weil class
zbMATH Keywords: triangulations
zbMATH Keywords: classifying maps
zbMATH Keywords: combinatorial Gauss map
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4192669