The Poincaré-Hopf theorem for line fields revisited

DOI10.1016/j.geomphys.2017.03.011zbMath1370.57011arXiv1612.04073OpenAlexW2561185665MaRDI QIDQ2628388

Mark Grant, Diarmuid J. Crowley

Publication date: 1 June 2017

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.04073

zbMATH Keywords

topological defectscondensed matter physicsline fieldsPoincaré-Hopf theorem

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Degree, winding number (55M25) Liquid crystals (76A15) Applications of global differential geometry to the sciences (53C80) Topology of vector bundles and fiber bundles (57R22)

Cites Work

• Line fields with branch defects
• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.
• Concordance and bordism of line fields
• A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
• Line element fields and Lorentz structures on differentiable manifolds
• On the Kunneth Formula and Functorial Dependence in Algebraic Topology
• The Gauss-Bonnet Theorem for Riemannian Polyhedra
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