The East Midlands in 2010: sub-regional profiles

The East Midlands in 2010 is the updated evidence base that supports the regional economic strategy, A Flourishing Region. This document presents detailed analysis of the East Midlands' sub-regions.

The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Entrepreneurship, innovation and the triple helix model: evidence from Oxfordshire and Cambridgeshire

This paper focuses on how regions become entrepreneurial and the extent to which the actors in the triple helix model are dominant at particular stages in development. It uses the case studies of Oxfordshire and Cambridgeshire in the UK to explore this theme. Both can now be described as ‘regional triple helix spaces’ (Etzkowitz 2008), and form two points of the Golden Triangle of Oxford, Cambridge and London universities. As entrepreneurial regions, however, they differ in a number of respects. This is not surprising given their differing geo-historical contexts. However, by comparing the two similar counties but which have their own distinctive features we are able to explore different dynamics which lead to the inception, implementation, consolidation and renewal (Etzkowitz and Klofsten 2005) of regions characterised by very high levels of technology-based entrepreneurship

The East Midlands in 2010

The East Midlands in 2010 is the updated evidence base that supports the regional economic strategy, A Flourishing Region. It presents a statistical portrait of the region covering demography, housing, economy & productivity, the labour market, deprivation & economic inclusion, transport, infrastructure & development, the environment and the spatial structure of the economy along with a series of sub-regional profiles

The topology of moduli spaces of free group representations

For any complex affine reductive group G and a fixed choice of maximal compact subgroup K, we show that the G-character variety of a free group strongly deformation retracts to the corresponding K-character space, which is a real semi-algebraic set. Combining this with constructive invariant theory and classical topological methods, we show that the SL(3,C)-character variety of a rank 2 free group is homotopic to an 8 sphere and the SL(2,C)-character variety of a rank 3 free group is homotopic to a 6 sphere.Comment: 37 pages, 2 figures, version 2 corrects typos, generalizes context, and adds a corollary, it is the accepted version to appear in Mathematische Annale

Making sense of eating, weight and risk in the early teenage years: views and concerns of parents in poorer socio-economic circumstances

Peer reviewe