Some examples of aspherical 4-manifolds that are homology 4-spheres
In this paper, Problem 4.17 on R. Kirby's problem list is solved by constructing infinitely many aspherical 4-manifolds that are homology 4-spheres
math.GT↗
arXiv subjects
Steven T. Tschantz
Publications and source records attributed to Steven T. Tschantz.
Integral Congruence Two Hyperbolic 5-Manifolds
In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form $H^5/Γ$ where $Γ$ is a torsion-free subgroup of minimal index of the congruence two subgroup $Γ^5_2$ of the group $Γ^5$ of positive units of the Lorentzian quadratic form $x_1^2+...+x_5^2-x_6^2$. We also show that $Γ^5_2$ is a reflection group with respect to a 5-dimensional right-angled convex polytope in $H^5$. As an application, we construct a hyperbolic 5-manifold of smallest known volume $7ζ(3)/4$.
math.GT↗
On the Growth of the Number of Hyperbolic Gravitational Instantons with respect to Volume
In this paper, we show that the number of hyperbolic gravitational instantons grows superexponentially with respect to volume. As an application, we show that the Hartle-Hawking wave function for the universe is infinitely peaked at a certain closed hyperbolic 3-manifold.
gr-qc↗
Semistability of amalgamated products, HNN-extensions, and all one-relator groups
The authors announce the following theorem. Theorem 1. If $G=A*_H B$ is an amalgamated product where $A$ and $B$ are finitely presented and semistable at infinity, and $H$ is finitely generated, then $G$ is semistable at infinity. If $G=A*_H$ is an HNN-extension where $A$ is finitely presented and semistable at infinity, and $H$ is finitely generated, then $G$ is semistable at infinity.
math.GR↗