The Minimal Dimension of a Sphere with an Equivariant Embedding of the Bouquet of g Circles is $$2g-1$$

Abstract

To embed the bouquet of $g$ circles $B_g$ into the $n$-sphere $S^n$ so that its full symmetry group action extends to an orthogonal actions on $S^n$, the minimal $n$ is $2g-1$. This answers a question raised by B. Zimmermann.