Cohomology of Fuchsian Groups and Non-Euclidean Crystallographic Groups

For each geometrically finite 2-dimensional non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we also determine the ring structure of the cohomology.Comment: 18 pages, updated with the referees' comment

On the equivariant KK- and KOKO-homology of some special linear groups

We compute the equivariant $KO$-homology of the classifying space for proper actions of $\textrm{SL}_3(\mathbb{Z})$ and $\textrm{GL}_3(\mathbb{Z})$. We also compute the Bredon homology and equivariant $K$-homology of the classifying spaces for proper actions of $\textrm{PSL}_2(\mathbb{Z}[\frac{1}{p}])$ and $\textrm{SL}_2(\mathbb{Z}[\frac{1}{p}])$ for each prime $p$. Finally, we prove the Unstable Gromov-Lawson-Rosenberg Conjecture for a large class of groups whose maximal finite subgroups are odd order and have periodic cohomology.Comment: 21 pages. Corrected typos and added some more examples in Section 6. To appear in Algebraic and Geometric Topolog

Negotiating access into firms: obstacles and strategies

Researchers often experience difficulties with the negotiation of access into firms for the purpose of data collection. The question we explore is: What are the main obstacles associated with access negotiation into firms; and what strategies do researchers employ to increase their chances of success? Our research work on the tendering process of contractors took place between 2006 and 2008. We successfully negotiated access into four firms (two each in Ghana and the UK) to observe live examples of tender preparation The techniques we employed in negotiating access were personal contacts, contacting firms through online details and professional institutions, etc. With all of this effort, our average success rate was less than 5 per cent. The main obstacles encountered were firms’ reluctance because of commercial sensitiveness and fear that the data could eventually be divulged to their competitors or end up in the public domain. However, some firms agreed mainly because of the written assurances of confidentiality and anonymity in reporting the study; reputation of the researchers’ academic institution; gatekeepers who spoke to their colleagues on our behalf; academic purpose of the study; and a feedback report which was promised in return for access to the case studies. Although the access through personal contacts is by far the easiest, it is not always possible. Researchers can approach firms as complete strangers, especially in a foreign country, and that could make the firms more likely to assist the research

BNSR invariants and ℓ2\ell^2-homology

We prove that if the $n$th $\ell^2$-Betti number of a group is non-zero then its $n$th BNSR invariant over $\mathbb{Q}$ is empty, under suitable finiteness conditions. We apply this to answer questions of Friedl--Vidussi and Llosa Isenrich--Py about aspherical K\"ahler manifolds, to verify some cases of the Singer Conjecture, and to compute certain BNSR invariants of poly-free and poly-surface groups.Comment: 31 pages, comments welcome

The character table of a sharply 5-transitive subgroup of Alt(12){\rm Alt}(12)

In this paper we calculate the character table of a sharply $5$-transitive subgroup of ${\rm Alt}(12)$, and of a sharply $4$-transitive subgroup of ${\rm Alt}(11)$. Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu groups, and instead deduce the desired character tables using only the existence of the stated multiply transitive permutation representations.Comment: 12 pages; submitte

On profinite rigidity amongst free-by-cyclic groups I: the generic case

We prove that amongst the class of free-by-cyclic groups, Gromov hyperbolicity is an invariant of the profinite completion. We show that whenever $G$ is a free-by-cyclic group with first Betti number equal to one, and $H$ is a free-by-cyclic group which is profinitely isomorphic to $G$, the ranks of the fibres and the characteristic polynomials associated to the monodromies of $G$ and $H$ are equal. We further show that for hyperbolic free-by-cyclic groups with first Betti number equal to one, the stretch factors of the associated monodromy and its inverse is an invariant of the profinite completion. We deduce that irreducible free-by-cyclic groups with first Betti number equal to one are almost profinitely rigid amongst irreducible free-by-cyclic groups. We use this to prove that generic free-by-cyclic groups are almost profinitely rigid amongst free-by-cyclic groups. We also show a similar results for {universal Coxeter}-by-cyclic groups.Comment: 38 page

Homological growth of Artin kernels in positive characteristic

We prove an analogue of the Lück Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups and Bestvina–Brady groups. Specifically, we prove that the mod p homology growth equals the dimension of the group homology with coefficients in a certain universal division ring and this is independent of the choice of residual chain. For general RFRS groups we obtain an inequality between the invariants. We also consider a number of applications to fibring, amenable category, and minimal volume entropy

Homological growth of Artin kernels in positive characteristic

We prove an analogue of the L\"uck Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups and Bestvina--Brady groups. Specifically, we prove that the mod $p$ homology growth equals the dimension of the group homology with coefficients in a certain universal division ring and this is independent of the choice of residual chain. For general RFRS groups we obtain an inequality between the invariants. We also consider a number of applications to fibring, amenable category, and minimal volume entropy.Comment: 23 pages. Section 4 is ne

Wave intensity analysis: A novel non-invasive method for determining arterial wave transmission

Wave intensity analysis is a novel technique for assessing wavelet transmission in the cardiovascular system. Using this tool, we have developed non-invasive techniques to study wave transmission in both central & peripheral arteries in man. The aim of this study was to determine the reproducibility of various haemodynamic measures in the carotid, brachial and radial arteries. 12 treated hypertensive men underwent applanation tonometry and pulsed Doppler ultrasound studies of the carotid, brachial and radial arteries on 2 occasions. Coefficients of variation for the local wave speed, cardiac compression wave intensity and main reflected wave intensity ranged between 3.7-6.6%, 8.2-11.4% and 12.5-19.6% respectively. We conclude that non-invasive methods used for wave intensity analysis are reproducible & provide additional information regarding the complex phenomenon of arterial wave transmission in man

The first ℓ2\ell^2-Betti number and groups acting on trees

We generalise results of Thomas, Allcock, Thom-Petersen, and Kar-Niblo to the first $\ell^2$-Betti number of quotients of certain groups acting on trees by subgroups with free actions on the edge sets of the graphs.Comment: 6 page