Related papers: Some Properties of Finitely Presented Groups with …
We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.
We prove a variant of the well-known Reidemeister-Schreier theorem for finitely $L$-presented groups. More precisely, we prove that each finite index subgroup of a finitely $L$-presented group is itself finitely $L$-presented. Our proof is…
The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable…
We discuss two aspects of the presentation of the theory of principal infinity-bundles in an infinity-topos, introduced in [NSSa], in terms of categories of simplicial (pre)sheaves. First we show that over a cohesive site C and for G a…
We associate with every locally expanding self-covering $f:M\to M$ of a compact path connected metric space a finitely presented group $V_f$. We prove that this group is a complete invariant of the dynamical system: two groups $V_{f_1}$ and…
We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
In this article we study two "strong" topologies for spaces of smooth functions from a finite-dimensional manifold to a (possibly infinite-dimensional) manifold modeled on a locally convex space. Namely, we construct Whitney type topologies…
We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…
If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by E(X).…
Given a compact cube complex $X$ that splits as a graph of virtually special cube complexes. Suppose that the fundamental groups of edge spaces are cyclonormal in the fundamental groups of adjacent vertex spaces. We show that $\pi_1X$ has…
We compare finiteness properties of locally compact groups that generalize the properties of being compactly generated and of being compactly presented. Three such families of properties have been proposed: Abels--Tiemeyer's type $C_n$,…
Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.
A linear system on a smooth complex algebraic surface gives rise to a family of smooth curves in the surface. Such a family has a topological monodromy representation valued in the mapping class group of a fiber. Extending arguments of…
A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…
Let $G$ be a finitely presented group. A new complexity called \textit{Karoubi-Weibel complexity} or \textit{covering type}, is defined for $G$. The construction is inspired by recent work of Karoubi and Weibel \cite{KW}, initially applied…
Big mapping class groups are the mapping class groups of infinite-type surfaces, that is, surfaces whose fundamental groups are not finitely generated. While mapping class groups of finite-type surfaces have been extensively studied, the…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…