Vol. 2, No. 2, 2009

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The index of a vector field on an orbifold with boundary

Elliot Paquette and Christopher Seaton

Vol. 2 (2009), No. 2, 161–175
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.

Keywords
orbifold, orbifold with boundary, Euler–Satake characteristic, Poincare–Hopf theorem, vector field, vector field index, Morse index, orbifold double
Mathematical Subject Classification 2000
Primary: 55R91, 57R12, 57R25
Milestones
Received: 11 June 2008
Accepted: 19 February 2009
Published: 7 May 2009

Communicated by Michael Dorff
Authors
Elliot Paquette
University of Washington
Department of Mathematics
Box 354350
Seattle, WA 98195-4350
United States
Christopher Seaton
Department of Mathematics and Computer Science
Rhodes College
2000 N. Parkway
Memphis, TN 38112
United States
http://faculty.rhodes.edu/seaton/