Related papers: On Finite domination and Poincar\'e duality

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group…

We initiate the study of profinite groups of non-negative deficiency. The principal focus of the paper is to show that the existence of a finitely generated normal subgroup of infinite index in a profinite group $G$ of non-negative…

Let $R$ be a noetherian normal domain. We investigate when $R$ admits a faithful module whose endomorphism ring has finite global dimension. This can be viewed as a non-commutative desingularization of $\Spec(R)$. We show that the existence…

In this paper we address the relation between the orbifold fundamental group and the topology of the underlying space. In particular, under the assumption that the orbifold fundamental group is equal to the fundamental group of the…

In this article, we introduce and develop the notion of parametrised Poincar\'{e} duality in the formalism of parametrised higher category theory by Martini-Wolf, in part generalising Cnossen's theory of twisted ambidexterity to the…

A topological space (not necessarily simply connected) is said to have finite homotopy rank-sum if the sum of the ranks of all higher homotopy groups (from the second homotopy group onward) is finite. In this article, we consider Stein…

We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite $p$th power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global…

Grothendieck-Verdier duality is a powerful and ubiquitous structure on monoidal categories, which generalises the notion of rigidity. Hopf algebroids are a generalisation of Hopf algebras, to a non-commutative base ring. Just as the…

We establish a method for calculating the Poincar\'e series of moduli spaces constructed as quotients of smooth varieties by suitable non-reductive group actions; examples of such moduli spaces include moduli spaces of unstable vector or…

The problem of the classification of the indefinite binary quadratic forms with integer coefficients is solved introducing a special partition of the de Sitter world, where the coefficients of the forms lie, into separate domains. Every…

Following a formula found in the paper of Avramov, Iyengar, Lipman, and Nayak (2010) and ideas of Neeman and Khusyairi, we indicate that Grothendieck duality for finite tor-amplitude maps can be developed from scratch via the formula $f^!…

We show that the class of profinite duality groups is closed under group extensions provided that the kernel satisfies some finiteness condition. This extends earlier results of Pletch and of Wingberg.

We show that provided $n\ne 3$, the involutive Hopf *-algebra $A_u(n)$ coacting universally on an $n$-dimensional Hilbert space has enough finite-dimensional representations in the sense that every non-zero element acts non-trivially in…

Let $P$ be a commutative Noetherian ring and $F$ be a self-dual acyclic complex of finitely generated free $P$-modules. Assume that $F$ has length four and $F_0$ has rank one. We prove that $F$ can be given the structure of a Differential…

We introduce the notion of a semifree isovariant $G$-Poincar\'e space, a homotopical notion interpolating between semifree closed smooth $G$-manifolds and the equivariant Poincar\'e spaces of [HKK24b]. It carries the additional structure of…

We define, for any group $G$, finite approximations ; with this tool, we give a new presentation of the profinite completion $\hat{\pi} : G \to \hat{G}$ of an abtract group $G$. We then prove the following theorem : if $k$ is a finite prime…

A set $A$ is dually Dedekind finite if every surjection from $A$ onto $A$ is injective; otherwise, $A$ is dually Dedekind infinite. An amorphous set is an infinite set that cannot be partitioned into two infinite subsets. A strictly…

We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct…

We construct an extension of the Poincare group which involves a mixture of internal and space-time supersymmetries. The resulting group is an extension of the superPoincare group with infinitely many generators which carry internal and…

We produce a fully faithful functor from finite type nilpotent spaces to cosimplicial binomial rings, thus giving an algebraic model of integral homotopy types. As an application, we construct an integral version of the…