Related papers: The cohomological restriction map and FP-infinity …

We prove that there are examples of finitely generated groups G together with group ring elements Q \in \bbQ G for which the von Neumann dimension \dim_{LG}\ker Q is irrational, so (in conjunction with other known results) answering a…

We study the realization problem of finite groups as the group of homotopy classes of self-homotopy equivalences of finite spaces. Let $G$ be a finite group. Using an infinite family of pairwise non weakly homotopic asymmetric spaces we…

We prove that rational homology of the Torelli group of genus g is infinite dimensional, provided g>6. This means that rational homology of the Torelli space of genus g>6 is infinite dimensional. The Torelli groups with marked points are…

Let R be any ring (with 1), \Gamma a group and R\Gamma the corresponding group ring. Let Ext_{R\Gamma}^{*}(M,M) be the cohomology ring associated to the R\Gamma-module M. Let H be a subgroup of finite index of \Gamma. The following is a…

We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up to symmetry. Our class includes many important examples…

We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by…

Let $G$ be a reductive group over a number field $F$, which is split at a finite place $\mathfrak{p}$ of $F$, and let $\pi$ be a cuspidal automorphic representation of $G$, which is cohomological with respect to the trivial coefficient…

We give a new characterisation of virtually free groups using graph minors. Namely, we prove that a finitely generated, infinite group is virtually free if and only if for any finite generating set, the corresponding Cayley graph is minor…

Let R be a commutative ring. If P is a maximal ideal of R whose a power is finitely generated then we prove that P is finitely generated if R is either locally coherent or arithmetical or a polynomial ring over a ring of global dimension…

Let SI(S_g) denote the hyperelliptic Torelli group of a closed surface S_g of genus g. This is the subgroup of the mapping class group of S_g consisting of elements that act trivially on H_1(S_g;Z) and that commute with some fixed…

We use assembly maps to study $\mathbf{TC}(\mathbb{A}[G];p)$, the topological cyclic homology at a prime $p$ of the group algebra of a discrete group $G$ with coefficients in a connective ring spectrum $\mathbb{A}$. For any finite group, we…

We give a lower bound for the exponent of certain elements in the integral cohomology of the total spaces of principal BC-bundles for C a finite cyclic group. As applications we give a proof of the theorem of A. Adem and H.-W. Henn that a…

We show that for any finitely generated subgroup $H$ of a limit group $L$ there exists a finite-index subgroup $K$ containing $H$, such that $K$ is a subgroup of a group obtained from $H$ by a series of extensions of centralizers and free…

Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$ and $M, N$ two finitely generated $R$-modules. By using a spectral sequence argument, it is shown that if either $\mathrm{dim}_RM\leq2$ and $\mathrm{H}^{i}_\mathfrak{a}(N)$…

We prove that $\textbf{SL}_3(\mathbb{Z}[t])$ has a finite index subgroup $\Gamma$ such that $H^2(\Gamma; \mathbb{Q})$ is infinite dimensional. The proof uses the geometry of the Euclidean building for $\textbf{SL}_3(\mathbb{Q}((t^{-1})))$.

Every countable group $G$ can be embedded in a finitely generated group $G^*$ that is hopfian and complete, i.e. $G^*$ has trivial centre and every epimorphism $G^*\to G^*$ is an inner automorphism. Every finite subgroup of $G^*$ is…

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and its…

We show that problems which have finite integer index and satisfy a requirement we call treewidth-bounding admit linear kernels on the class of $H$-topological-minor free graphs, for an arbitrary fixed graph $H$. This builds on earlier…

We investigate bounds on the dimension of cohomology groups for finite groups acting on an irreducible kG-module for G a finite group of bound sectional p-rank and k an algebraically closed field of characteristic p.

Consider the configuration spaces of manifolds. We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unordered configuration spaces of manifolds with non-trivial…