Related papers: Cohomology on the centric orbit category of a fusi…

The fusion orbit category $\overline{\mathcal F _{\mathcal C}} (G)$ of a discrete group $G$ over a collection $\mathcal C$ is the category whose objects are the subgroups $H$ in $\mathcal C$, and whose morphisms $H \to K$ are given by the…

We study higher limits over the centric orbit category of a fusion system realized by an amalgamated product. In so doing we provide a novel technique for studying the Diaz-Park sharpness conjecture and prove it (in the case of the…

We study the higher derived functors of the inverse limit of a functor F: D --> Z_{(p)}-mod, where D is one of the standard categories which arise when studying the homotopy theory of the classifying space of a finite group G, e.g., the…

We prove that an isomorphism between saturated fusion systems over the same finite p-group is detected on the elementary abelian subgroups of the hyperfocal subgroup if p is odd, and on the abelian subgroups of the hyperfocal subgroup of…

We develop tools which use common fusion systems building techniques in order to compute higher limits over the centric orbit category. We apply these tools in order to study both the Diaz-Park sharpness conjecture as well as the weaker…

In this short note we study the cohomology algebra of saturated fusion systems using finite groups which realize saturated fusion systems and Hochschild cohomology of group algebras. A similar result to a theorem of Alperin is proved for…

We study the D\'iaz-Park sharpness conjecture for fusion systems and prove that, under certain circumstances, there exists a 4 terms exact sequence relating the first two higher limits of the contravariant part of a Mackey functor over…

Let G be a group of type FP_n and let p>1. In this paper we show that the reduced l^p-homology of G is dual to the reduced l^q-cohomology for \frac{1}{p}+\frac{1}{q}=1. In our main theorem we show that for a group of type FP_n with a…

We give an algebraic proof for a theorem of Mislin in the case of cohomology of saturated fusion systems defined on p-groups when p is odd. Some applications of this theorem to block algebras of finite groups are also given.

We show that if an inclusion of finite groups H < G of index prime to p induces a homeomorphism of mod p cohomology varieties, or equivalently an F-isomorphism in mod p cohomology, then H controls p-fusion in G, if p is odd. This…

We extend Dwyer's sharp subgroup homology decomposition of the classifying space of a finite group to arbitrary saturated fusion systems and arbitrary Mackey functors.

Let $G$ be a finite group and $k$ a field of characteristic $p$. We conjecture that if $M$ is a $kG$-module with $H^*(G,M)$ finitely generated as a module over $H^*(G,k)$ then as an element of the stable module category…

We obtain vanishing ranges for the mod $p$ cohomology of alternating subgroups of finite $p$-free Coxeter groups. Here a Coxeter group $W$ is $p$-free if the order of the product $st$ is prime to $p$ for every pair of Coxeter generators…

The aim of the current paper is to explore the implications on the group $G$ of the non-vanishing of the cohomology in degree one of one of its representation $\pi$, given some mixing conditions on $\pi$. In one direction, harmonic cocycles…

We study saturated fusion systems on $p$-groups having sectional rank $3$ for all odd primes $p$. For $p\geq 5$, we obtain a complete classification of the ones that do not have any non-trivial normal $p$-subgroups.

Let $\Gamma_{0,n}^+(p)\subset \mathrm{SL}_n(\mathbb{Z})$ be the congruence subgroup of level-$p$ whose first column is of the form $(*,0,\dots,0)^t\bmod p$. We prove that the top-dimensional cohomology group…

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 give another proof of an observation of Th\'evenaz \cite{T1989} and present a fusion system version of it. Namely, for a saturated fusion system $\CF$ on a finite $p$-group $S$, we show that the number of the $\CF$-conjugacy classes of…

We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the…

The action of the mapping class group $\mathrm{Mod}_g$ of an oriented surface $\Sigma_g$ on the lower central series of $\pi_1(\Sigma_g)$ defines the descending filtration in $\mathrm{Mod}_g$ called the Johnson filtration. The first two…