The Poincare-Hopf Theorem for line fields revisited

A Poincare-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopfs 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2k >= 4. In 1984 Janich presented a Poincare-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincare-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions. (C) 2017 Elsevier B.V. All rights reserved.