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Equivalence of cyclic $p$-squared actions on handlebodies. (arXiv:1704.08355v1 [math.AT])
来源于:arXiv
In this paper we consider all orientation-preserving
$\mathbb{Z}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus $g>0$
for $p$ an odd prime. To do so, we examine particular graphs of groups
$(\Gamma($v$),\mathbf{G(v)})$ in canonical form for some 5-tuple v
$=(r,s,t,m,n)$ with $r+s+t+m>0$. These graphs of groups correspond to the
handlebody orbifolds $V(\Gamma($v$),{\mathbf{G(v)}})$ that are homeomorphic to
the quotient spaces $V_g/\mathbb{Z}_{p^2}$ of genus less than or equal to $g$.
This algebraic characterization is used to enumerate the total number of
$\mathbb{Z}_{p^2}$-actions on such handlebodies, up to equivalence. 查看全文>>