2 citations · 3 across the 9 of their papers we have counts for
11 papers
Bounded cohomology, Codimension two submanifolds and Pontryagin-Thom constructions
Thorben Kastenholz
In this note we develop a novel approach for proving the non-vanishing of bounded cohomology. This utilizes a splitting argument whose simplest form is as follows: Let M denote an…
Simplicial volume of open books in dimension 4
Thorben Kastenholz
In this short note we adapt a proof by Bucher and Neofytidis to prove that the simplicial volume of 4-manifolds admitting an open book decomposition vanishes. In particular this sh…
Non vanishing of the fourth bounded cohomology of free groups and codimension 2 subspaces
Thorben Kastenholz
In this note we prove that the fouth bounded cohomology of non-abelian free groups with trivial real coefficients is non-zero. In order to prove this, we establish a splitting argu…
Simplicial volume of manifolds fibering with connected structure group
Thorben Kastenholz
In this note we investigate the simplicial volume of fiber bundles with connected structure group. We are able to show that if the structure group is either compact or a Lie group,…
Simplicial bounded cohomology and stability
Thorben Kastenholz, Robin J. Sroka
We introduce a set of combinatorial techniques for studying the simplicial bounded cohomology of semi-simplicial sets, simplicial complexes and posets. We apply these methods to pr…
Symplectic Groups, Mapping Class Groups and the Stability of Bounded Cohomology
Thorben Kastenholz
Mapping class groups satisfy cohomological stability. In this note we show how results by Bestvina and Fujiwara imply that the bounded cohomology does not stabilize, additionally w…
The minimal genus problem for right angled Artin groups
Rachael Boyd, Thorben Kastenholz, Jean Pierre Mutanguha
We investigate the minimal genus problem for the second homology of a right angled Artin group (RAAG). Firstly, we present a lower bound for the minimal genus of a second homology…
Simplicial volume and essentiality of manifolds fibered over spheres
Thorben Kastenholz, Jens Reinhold
We study the question when a manifold that fibers over a sphere can be rationally essential, or even have positive simplicial volume. More concretely, we show that mapping tori of…
The Minimal Genus of Homology Classes in a Finite 2-Complex
Thorben Kastenholz, Mark Pedron
We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result i…
Homological Stability for Spaces of Subsurfaces with Tangential Structure
Thorben Kastenholz
Given a manifold with boundary, one can consider the space of subsurfaces of this manifold meeting the boundary in a prescribed fashion. It is known that these spaces of subsurface…
Exponential Torsion Growth for Random 3-Manifolds
Hyungryul Baik, David Bauer, Ilya Gekhtman +5
We show that a random 3-manifold with positive first Betti number admits a tower of cyclic covers with exponential torsion growth.