• Corpus ID: 59936439

Equivariant hyperbolization of $3$-manifolds via homology cobordisms

@article{Auckly2018EquivariantHO,
  title={Equivariant hyperbolization of \$3\$-manifolds via homology cobordisms},
  author={Dave Auckly and Hee Jung Kim and P. Melvin and Daniel Ruberman},
  journal={arXiv: Geometric Topology},
  year={2018}
}
The main result of this paper is that any $3$-dimensional manifold with a finite group action is equivariantly, invertibly homology cobordant to a hyperbolic manifold; this result holds with suitable twisted coefficients as well. The following two consequences motivated this work. First, there are hyperbolic equivariant corks (as defined in previous work of the authors) for a wide class of finite groups. Second, any finite group that acts on a homology $3$-sphere also acts on a hyperbolic… 
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