## Involve: A Journal of Mathematics

• Involve
• Volume 2, Number 2 (2009), 161-175.

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

#### 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.

#### Article information

Source
Involve, Volume 2, Number 2 (2009), 161-175.

Dates
Accepted: 19 February 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513799138

Digital Object Identifier
doi:10.2140/involve.2009.2.161

Mathematical Reviews number (MathSciNet)
MR2501335

Zentralblatt MATH identifier
1175.57022

#### Citation

Paquette, Elliot; Seaton, Christopher. The index of a vector field on an orbifold with boundary. Involve 2 (2009), no. 2, 161--175. doi:10.2140/involve.2009.2.161. https://projecteuclid.org/euclid.involve/1513799138

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