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Discrete group actions on 3-manifolds and embeddable Cayley complexes
- Publication Year :
- 2022
-
Abstract
- We prove that a group $\Gamma$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $\Gamma$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the following four 3-manifolds: (i) $\mathbb{S}^3$, (ii) $\mathbb{R}^3$, (iii) $\mathbb{S}^2 \times \mathbb{R}$, (iv) the complement of a tame Cantor set in $\mathbb{S}^3$.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.09918
- Document Type :
- Working Paper