Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-6127
Main Title: Complex line bundles over simplicial complexes and their applications
Author(s): Knöppel, Felix
Pinkall, Ulrich
Type: Book Part
Language Code: en
Is Part Of: 10.1007/978-3-662-50447-5
Abstract: Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of André Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise-constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension.
URI: http://depositonce.tu-berlin.de/handle/11303/6686
http://dx.doi.org/10.14279/depositonce-6127
Issue Date: 2016
Date Available: 1-Sep-2017
DDC Class: 510 Mathematik
Creative Commons License: https://creativecommons.org/licenses/by-nc/2.5/
Book Title: Advances in discrete differential geometry
Publisher: Springer
Publisher Place: Berlin, Heidelberg
Publisher DOI: 10.1007/978-3-662-50447-5_6
Page Start: 197
Page End: 239
ISBN: 978-3-662-50447-5
Appears in Collections:Technische Universität Berlin » Fakultäten & Zentralinstitute » Fakultät 2 Mathematik und Naturwissenschaften » Institut für Mathematik » Publications

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