Year: 2026
Type: preprint
Abstract: For a closed, oriented 3-manifold $M$, we show that any finite subgroup of its mapping class group preserves an isotopy class of filling sphere system on $M$. This is an isotopy version of the "equivariant sphere theorem" of Meeks-Yau. As part of our analysis, we establish a bijection between simplices of the Guirardel--Levitt outer space for $π_1(M)$ and filling sphere systems in $M$, generalizing an argument of Hatcher. We also compute the image of $\mathrm{Homeo}(M)\to\mathrm{Out}(π_1M)$ for any such $M$.
Source: arXiv (Cornell University)
Authors: Bregman, Corey, Tshishiku, Bena
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223676988