The minimal dimension of a sphere with an equivariant embedding of the bouquet of $g$ circles is $2g-1$

Zhongzi Wang

doi:10.1007/s00454-021-00300-9

paper

The minimal dimension of a sphere with an equivariant embedding of the bouquet of $g$ circles is $2 g - 1$

arXiv:2203.16830 · doi:10.1007/s00454-021-00300-9

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 $2 g - 1$ . This answers a question raised by B. Zimmermann.

9 pages, 4 figures, To appear in Discrete Comput. Geom

The minimal dimension of a sphere with an equivariant embedding of the bouquet of g circles is 2g−1

Abstract

The minimal dimension of a sphere with an equivariant embedding of the bouquet of $g$ circles is $2 g - 1$