相关论文: Length functions on mapping class groups and simpl…

We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The…

We introduce a combinatorial property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a canonical finite presentation. We also define…

In continuation of [3] we discuss metrics of the form $$ G^P_f(h,k)=\int_M \sum_{i=0}^p\Phi_i(\Vol(f)) \g((P_i)_fh,k) \vol(f^*\g) $$ on the space of immersions $\Imm(M,N)$ and on shape space $B_i(M,N)=\Imm(M,N)/\on{Diff}(M)$. Here $(N,\g)$…

We study moduli spaces of flat metrics on closed Riemannian orbifolds admitting such metrics. We show that for such orbifolds $\mathcal{O}$, the Teichm\"uller space of flat metrics $\mathcal{T}_{\text{flat}}(\mathcal{O})$ serves as a…

Invariant tori are prominent features of symplectic and volume preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an $n$-dimensional…

Let $(M^{n+1},g)$ be a closed Riemannian manifold of dimension $3\le n+1\le 5$. We show that, if the metric $g$ is generic or if the metric $g$ has positive Ricci curvature, then $M$ contains infinitely many geometrically distinct constant…

In this study, we prove that the actions of the mapping class groups on a large range of higher Teichm\"uller spaces with a rank of at least two possess infinite Atiyah-Bott-Goldman covolume. This result encompasses $\mathsf{G}$-Hitchin…

We study an intrinsic volume form defined on a pseudoconvex hypersurface in a complex Calabi-Yau manifold. We compute first and second variation formulae and discuss possible analogues of the affine isoperimetric inequality. In the last…

We study random elements of subgroups (and cosets) of the mapping class group of a closed hyperbolic surface, in part through the properties of their mapping tori. In particular, we study the distribution of the homology of the mapping…

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…

Filling invariants are measurements of a metric space describing the behaviour of isoperimetric inequalities. In this article we examine filling functions and higher divergence functions. We prove for a class of stratified nilpotent Lie…

Using the locally compact abelian group $\BT \times \BZ$, we assign a meromorphic function to each ideal triangulation of a 3-manifold with torus boundary components. The function is invariant under all 2--3 Pachner moves, and thus is a…

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…

Let $\mathcal{E}$ denote the space of entire functions with the topology of uniform convergence on compact sets. The action of $\mathbb C$ by translations on $\mathcal E$ is defined by $T_zf(w) = f(w+z)$. Let $\mathcal{U}$ denote the set of…

This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that \pi_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at…

Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle $\mathrm{PSL}_2(\mathbb{Z})\backslash\mathrm{PSL}_2(\mathbb{R})$. The complement of any finite number of orbits is a…

A meromorphic inner function is a bounded holomorphic function in the upper half-plane which is unimodular on the real line and extends to a meromorphic function in the whole complex plane. The argument of a meromorphic inner function on…

We introduce volume forms on mapping stacks in derived algebraic geometry using a parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks we describe this volume form in terms of the Todd class. In the…

Lower bounds on Ricci curvature limit the volumes of sets and the existence of harmonic functions on Riemannian manifolds. In 1975, Shing Tung Yau proved that a complete noncompact manifold with nonnegative Ricci curvature has no…

A natural problem in the theory of 3-manifolds is the question of whether two 3-manifolds are homeomorphic or not. The aim of this paper is to study this problem for the class of closed Haken manifolds using degree one maps. To this purpose…