Exponential separation in 4-manifolds

Exponential Torsion Growth for Random 3-Manifolds

We show that a random 3-manifold with positive first Betti number admits a tower of cyclic covers with exponential torsion growth.

具有指数同调 torsion 增长的双曲流形族

Family of hyperbolic manifolds with exponential homology torsion growth

本文构造了双曲流形族，展示同调 torsion 的指数增长，证明最近关于同调 torsion 的界是渐近最优的。

Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds

For d=2n+1 a positive odd integer, we consider sequences of arithmetic subgroups of SO_0(d,1) and Spin(d,1) yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.

Exponential Iterated Integrals and the Relative Solvable Completion of the Fundamental Group of a Manifold

We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M can be expressed via these new integrals. The ring of exponential iterated integrals contains the coordinate rings for a class of universal representations, called relative solvable completions, of the fundamental group. We consider exponential iterated integrals in the particular case of fibered knot complements, where the fundamental group always has a fa…

Strong Jordan separation and applications to rigidity

We prove that simple, thick hyperbolic P-manifolds of dimension >2 exhibit Mostow rigidity. We also prove a quasi-isometry rigidity result for the fundamental groups of simple, thick hyperbolic P-manifolds of dimension >2. The key tool in the proofs of these rigidity results is a strong form of the Jordan separation theorem, for maps from S^n to S^{n+1} which are not necessarily injective.

Subgroup distortion of 3-manifold groups

In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is closely related to the separability of this subgroup.