arXiv subjects

Nick Wright

Publications and source records attributed to Nick Wright.

25 records · Page 2Linked to original sources

arXiv2013

Spaces of Graphs, Boundary Groupoids and the Coarse Baum-Connes Conjecture

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particular, we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree. We then connect the boundary conjecture to the coarse Baum-Connes conjecture using homological methods, which allows us to exhibit all the current uniformly discrete counterexamples to the coarse Baum-Connes conjecture in an elementary way.

math.KT↗

arXiv2013

K-theory and exact sequences of partial translation algebras

In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context. We apply this general framework to compute the K-theory of partial translation algebras and group C*-algebras in the context of almost invariant subspaces of discrete groups. This generalises the work of Cuntz, Lance, Pimsner and Voiculescu. In particular we provide a new perspective on Pimsner's calculation of the K-theory for a graph product of groups.

math.OA↗

arXiv2012

Constraints on the ubiquity of coronal X-ray cycles

Stellar activity cycles are known to be a widespread phenomenon amongst moderately active solar- and late-type stars from long-term periodic variations in chromospheric Ca II H and K emission lines, yet to date only a handful of coronal X-ray cycles are known. We have surveyed serendipitously observed stellar sources in fields observed multiple times in the last decade by XMM-Newton and present our analysis of 9 stars from 6 fields. Since our sample is flux-limited, it is strongly biased towards higher levels of X-ray activity. We fit a single temperature APEC spectrum to each source and search for significant periodicities using a Lomb-Scargle Periodogram (LSP). We use a Monte Carlo (MC) algorithm to yield robust analysis of the statistical significance of cycle detections and non-detections. None of the 9 stellar lightcurves show any convincing indications of periodicity. From MC simulations we simulate the detection capabilities of our methodology and, assuming a uniform distribution of cycle periods and strengths over the domain searched, we conclude with 95% confidence that less than 72% of the stars represented by our sample of active stars have 5-13 year coronal X-ray cycles.

astro-ph.SR↗

arXiv2010

Finite asymptotic dimension for CAT(0) cube complexes

In this paper we prove that the asymptotic dimension of a finite-dimensional CAT(0) cube complex is bounded above by the dimension. To achieve this we prove a controlled colouring theorem for the complex. We also show that every CAT(0) cube complex is a contractive retraction of an infinite dimensional cube. As an example of the dimension theorem we obtain bounds on the asymptotic dimension of small cancellation groups.

math.MG↗

arXiv2010

Amenable actions, invariant means and bounded cohomology

We show that topological amenability of an action of a countable discrete group on a compact space is equivalent to the existence of an invariant mean for the action. We prove also that this is equivalent to vanishing of bounded cohomology for a class of Banach G-modules associated to the action, as well as to vanishing of a specific cohomology class. In the case when the compact space is a point our result reduces to a classic theorem of B.E. Johnson characterising amenability of groups. In the case when the compact space is the Stone-Čech compactification of the group we obtain a cohomological characterisation of exactness for the group, answering a question of Higson.

math.GR↗

arXiv2010

Pairings, duality, amenability and bounded cohomology

We give a new perspective on the homological characterisations of amenability given by Johnson in the context of bounded cohomology and by Block and Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterisations. We apply these ideas to give a new proof of non- vanishing for the bounded cohomology of a free group.

math.GR↗

arXiv2005

Exactness from Proper Actions

In this paper we show that if a discrete group $G$ acts properly isometrically on a discrete space $X$ for which the uniform Roe algebra $C_u^*(X)$ is exact then $G$ is an exact group. As a corollary, we note that if the action is cocompact then the following are equivalent: The space $X$ has Yu's property A; $C^*_u(X)$ is exact; $C_u^*(X)$ is nuclear.

math.OA↗