Equivariant path fields on topological manifolds

Lucilía D. Borsari, Fernanda S. P. Cardona, Peter Wong

DOI: http://dx.doi.org/10.12775/TMNA.2009.001

Abstract


A classical theorem of H. Hopf asserts that a closed connected smooth
manifold admits a nowhere vanishing vector field if and only if its
Euler characteristic is zero. R Brown generalized Hopf's result
to topological manifolds, replacing vector fields with path fields.
In this note, we give an equivariant analog of Brown's theorem for
locally smooth $G$-manifolds where $G$ is a finite group.

Keywords


Equivariant Euler characteristic; equivariant path fields; locally smooth G-manifolds

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