The index of a vector field on an orbifold with boundary

Details The index of a vector field on an orbifold with boundary The index of a vector field on an orbifold with boundary

2008-06-12

arxiv.org/abs/0806.2113v1

Involve, a Journal of Mathematics 2 (2009) 161--175

Mathematics

Differential Geometry

14 pages

Scientific paper

A Poincar\'{e}-Hopf theorem in the spirit of Pugh is proven for compact orbifolds with boundary. The theorem relates the index sum of a smooth vector field in generic contact with the boundary orbifold to the Euler-Satake characteristic of the orbifold and a boundary term. The boundary term is expressed as a sum of Euler characteristics of tangency and exit-region orbifolds. As a corollary, we express the index sum of the vector field induced on the inertia orbifold to the Euler characteristics of the associated underlying topological spaces.

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