arXiv subjects

Hartwig Senska

Publications and source records attributed to Hartwig Senska.

2 recordsLinked to original sources

arXiv2020

Homology bounds for hyperbolic orbifolds

We will provide bounds on both the Betti numbers and the torsion part of the homology of hyperbolic orbifolds. These bounds are linear in the volume and are a direct consequence of an efficient simplicial model of the thick part, which we will construct as well. The homology statements complement previous work of Bader, Gelander and Sauer (torsion homology of manifolds), Samet (Betti numbers of orbifolds) and a classical theorem of Gromov (Betti numbers of manifolds). For arithmetic, non-compact hyperbolic orbifolds -- i.e. in the case of arithmetic, non-uniform lattices in $\operatorname{Isom}(\mathbb{H}^n)$ -- the strongest results will be obtained.

math.GT↗

arXiv2019

Topological complexity of visibility manifolds

A recent result of Bader, Gelander and Sauer shows that for manifolds of pinched negative curvature, the torsion part of the homology can be controlled by the volume. This is done by constructing an efficient simplicial model of the thick part, which also provides another proof of the analogous statement for the free part of the homology, a classical theorem due to Gromov. We will extend these results to more general curvature conditions, namely the case where the sectional curvature can get arbitrarily close to zero, but the visibility axiom still holds.

math.GT↗