|
|||||
 |
|
|
|
|
|
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/ | |
|
