Related papers: Cost vs. integral foliated simplicial volume

In analogy with ordinary simplicial volume, we show that integral foliated simplicial volume of oriented closed connected aspherical $n$-manifolds that admit an open amenable cover of multiplicity at most $n$ is zero. This implies that the…

We establish an integration formula for integral foliated simplicial volume along ergodic decompositions. This is analogous to the ergodic decomposition formula for the cost of groups.

We observe that stable integral simplicial volume of closed manifolds gives an upper bound for the rank gradient of the corresponding fundamental groups.

Integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coefficients with the flexibility of measure spaces. In this article, using the language of measure equivalence of groups we prove a…

We show that the integral foliated simplicial volume of a connected compact oriented smooth manifold with a regular foliation by circles vanishes.

We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action…

We show that for $n \neq 1,4$ the simplicial volume of an inward tame triangulable open $n$-manifold $M$ with amenable fundamental group at infinity at each end is finite; moreover, we show that if also $\pi_1(M)$ is amenable, then the…

Integral simplicial volume is a homotopy invariant of oriented closed connected manifolds, defined as the minimal weighted number of singular simplices needed to represent the fundamental class with integral coefficients. We show that…

We give estimates of the Gromov norm of the top dimensional class in $H_c^4(\mathrm{Isom}(\mathbb{H}_{\mathbb{C}}^2);\mathbb{R})$. As a consequence, we obtain an explicit upper bound for the simplicial volume of closed oriented manifolds…

The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth $S^1$-action vanishes. In the present work we prove a version of this result for the integral foliated simplicial volume of aspherical…

Let N be a manifold (with boundary) of dimension at least 3, such that its interior admits a hyperbolic metric of finite volume. We discuss the possible limits arising from sequences of relative fundamental cycles approximating the…

We prove that cubical simplicial volume of oriented closed 3-manifolds is equal to one fifth of ordinary simplicial volume.

We compute the value of the simplicial volume for closed, oriented Riemannian manifolds covered by $\mathbb{H}^{2}\times\mathbb{H}^{2}$ explicitly, thus in particular for products of closed hyperbolic surfaces. This gives the first exact…

We introduce the stable presentation length of a finitely presented group. The stable presentation length of the fundamental group of a 3-manifold can be considered as an analogue of the simplicial volume. We show that the stable…

We show that the simplicial volume is superadditive with respect to gluings along certain submanifolds of the boundary. Our criterion applies to boundary connected sums and 1-handle attachments. Moreover, we generalize a well-known…

We provide sharp lower bounds for the simplicial volume of compact $3$-manifolds in terms of the simplicial volume of their boundaries. As an application, we compute the simplicial volume of several classes of $3$-manifolds, including…

We show that, in dimension at least $4$, the set of locally finite simplicial volumes of oriented connected open manifolds is $[0, \infty]$. Moreover, we consider the case of tame open manifolds and some low-dimensional examples.

We provide an estimate of the amenable category of oriented closed connected complete affine manifolds whose fundamental group contains an infinite amenable normal subgroup. As an application we show that all such manifolds have zero…

We give an elementary proof that, for a closed manifold with an integral-integral affine structure, its total volume and number of integral points coincide. The proof uses rational Ehrhart theory and elementary Fourier analysis to estimate…

Let $M$ be the interior of a connected, oriented, compact manifold $V$ of dimension at least 2. If each path component of $\partial V$ has amenable fundamental group, then we prove that the simplicial volume of $M$ is equal to the relative…