Symmetries of hyperbolic 4-manifolds

Abstract

In this paper, for each finite group $G$, we construct explicitly a non-compact complete finite-volume arithmetic hyperbolic $4$-manifold $M$ such that $\mathrm{Isom}M\cong G$, or ${\mathrm{Isom}}^{+}M\cong G$. In order to do so, we use essentially the geometry of Coxeter polytopes in the hyperbolic $4$-space, on one hand, and the combinatorics of simplicial complexes, on the other.

32 pages, 10 figures; Int. Math. Res. Notices (2015); SAGE worksheet available at https://doi.org/10.7910/DVN/0YUU6O; a minor mistake in the proof of Proposition 4.4 corrected in Proposition 2.5 / Remark 2.6 of arXiv:1710.07534

References in corpus (3)

• Coxeter groups, quiver mutations and geometric manifolds
• A geometrically bounding hyperbolic link complement
• Some hyperbolic 4-manifolds with low volume and number of cusps

Cited by in corpus (6)

• Hyperbolic four-manifolds, colourings and mutations
• Coxeter groups, quiver mutations and geometric manifolds
• The complement of the figure-eight knot geometrically bounds
• New hyperbolic 4-manifolds of low volume
• A small closed convex projective 4-manifold via Dehn filling
• Many cusped hyperbolic 3-manifolds do not bound geometrically