arXiv subjects

Ervin Hadziosmanovic

Publications and source records attributed to Ervin Hadziosmanovic.

5 recordsLinked to original sources

arXiv2026

The bounded area class of negatively curved surfaces

Let $S$ be an oriented surface, possibly of infinite type, endowed with a complete Riemannian metric with pinched negative curvature. We prove that the area form defines a non-trivial class in the second bounded cohomology group of $S$, unless $S$ is diffeomorphic to the disc or the cylinder. This is in sharp contrast with the $n$-dimensional case, $n>2$, where the non-triviality of the volume form in bounded cohomology is related to the Cheeger constant of the manifold. We also discuss how the bounded area class depends on the metric: we prove that, for compact surfaces, it recognizes constant curvature metrics among pinched negatively curved ones, while, even in the case of surfaces of infinite type, it does not distinguish non-isometric hyperbolic structures. More precisely, when $S$ is compact we show that, among the negatively curved structures of fixed area, the ones with constant curvature provide the unique minimizers for the norm of the bounded area class.

math.GT↗

arXiv2026

Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity

We prove that the outer automorphism group of a one-ended hyperbolic group is virtually a hierarchically hyperbolic group (HHG), under mild orientability conditions on the associated JSJ decomposition. This is done by proving that a finite-index subgroup is a central extension of a product of orbifold mapping class groups, and the extension has bounded Euler class. Our theorem is sharp: we exhibit a surface amalgam whose fundamental group has full outer automorphism group which is not a HHG.

math.GR↗

arXiv2026

Bounded volume class and Cheeger isoperimetric constant for negatively curved manifolds

We prove that for manifolds with negative curvature bounded away from $0$ of infinite volume and bounded geometry, the bounded fundamental class, defined via integration of the volume form over straight top-dimensional simplices, vanishes if and only if the Cheeger isoperimetric constant is positive. This gives a partial affirmative answer to a conjecture of Kim and Kim. Furthermore, we show that for all manifolds with negative curvature bounded away from $0$ of infinite volume, the positivity of the Cheeger constant implies the vanishing of the bounded volume class, solving one direction of the conjecture in full generality.

math.GT↗

arXiv2026

Bounded cohomology classes from differential forms

Let $M$ be a complete hyperbolic $n$-manifold, $n\geq 2$. Via integration over geodesic simplices, any closed bounded differential 2-form on $M$ defines a bounded cohomology class in $H^2_b(M)$. It was proved by Barge and Ghys (for $n=2$) and by Battista et al. (for $n>2$) that, if $M$ is closed, then this procedure defines an injective embedding of the (infinite-dimensional) space of closed differential $2$-forms on $M$ into $H^2_b(M)$. We extend this result to the case when the fundamental group of $M$ is of the first kind, i.e. its limit set is equal to the whole boundary at infinity of hyperbolic space (this holds, for example, when $M$ has finite volume). Our argument is different from Barge and Ghys' original one, and relies on the following fact of independent interest: an $L^\infty$ function on the hyperbolic plane is determined by its integrals over all ideal triangles. We prove this fact by way of Fourier analysis on the hyperbolic plane.

math.GT↗

arXiv2025

On the integral simplicial volume of cyclic covers of mapping tori

In this paper, we investigate the asymptotic behavior of the integral simplicial volume of cyclic covers of manifolds that fiber over the circle with fiber given by an $n$-dimensional torus. By studying the integral filling volume -- an invariant introduced by Frigerio and the first author -- for the monodromy, we establish both lower and upper bounds for the limit of the integral simplicial volume of these covers, normalized by the degree of the covering. These bounds are expressed in terms of the action of the monodromy on the real homology of the fiber. As applications, we establish a close connection between the topological entropy and the integral filling volume of self-homeomorphisms of $n$-dimensional tori, we find new examples for which the Delta-complexity and the integral simplicial volume are not equivalent, and we prove the nonvanishing of the filling volume for Anosov self-diffeomorphisms of infranilmanifolds.

math.GT↗