Abstract
A Poincaré–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.
Citation
Elliot Paquette. Christopher Seaton. "The index of a vector field on an orbifold with boundary." Involve 2 (2) 161 - 175, 2009. https://doi.org/10.2140/involve.2009.2.161
Information