Divergence and quasi-isometry classes of random Gromov’s monsters

Homological Invariants and Quasi - Isometry

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain that the cohomological dimension cdR over a commutative ring R satisfies the inequality cdR(Λ) ≤ cdR(Γ) if Λ embeds uniformly into Γ and cdR(Λ) < ∞ holds. Another consequence of our results is that the Hirsch ra...

On Asymptotic Cones and Quasi{isometry Classes of Fundamental Groups of 3-manifolds

Quasi-isometry rigidity of groups

2 Rigidity of non-uniform rank one lattices 6 2.1 Theorems of Richard Schwartz . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Finite volume real hyperbolic manifolds . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Proof of Theorem 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . ...

Isometry Classes of Indecomposable Linear Codes

In the constructive theory of linear codes, we can restrict attention to the isometry classes of indecomposable codes, as it was shown by Slepian. We describe these classes as orbits and we demonstrate how they can be enumerated using cycle index polynomials and the tools already incorporated in SYMMETRICA, a computer algebra package devoted to representation theory and combinatorics of symmetr...

On Rough-isometry Classes of Hilbert Geometries

We prove that Hilbert geometries on uniformly convex Euclidean domains with C 2-boundaries are roughly isometric to the real hyperbolic spaces of corresponding dimension.