### Equivariant path fields on topological manifolds

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.

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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