Involve: A Journal of Mathematics

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

The index of a vector field on an orbifold with boundary

Elliot Paquette and Christopher Seaton

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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

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

Received: 11 June 2008
Accepted: 19 February 2009
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R91: Equivariant fiber spaces and bundles [See also 19L47] 57R12: Smooth approximations 57R25: Vector fields, frame fields

orbifold orbifold with boundary Euler–Satake characteristic Poincare–Hopf theorem vector field vector field index Morse index orbifold double


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.

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