25 research outputs found

    Continuity properties of measurable group cohomology

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    A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic properties of group cohomology, but various analytic features of those cohomology groups were only partially understood. This paper re-examines some of those issues. At its heart is a simple dimension-shifting argument which enables one to `regularize' measurable cocycles, leading to some simplifications in the description of the cohomology groups. A range of consequences are then derived from this argument. First, we prove that for target modules that are Fr\'echet spaces, the cohomology groups agree with those defined using continuous cocycles, and hence they vanish in positive degrees when the acting group is compact. Using this, we then show that for Fr\'echet, discrete or toral modules the cohomology groups are continuous under forming inverse limits of compact base groups, and also under forming direct limits of discrete target modules. Lastly, these results together enable us to establish various circumstances under which the measurable-cochains cohomology groups coincide with others defined using sheaves on a semi-simplicial space associated to the underlying group, or sheaves on a classifying space for that group. We also prove in some cases that the natural quotient topologies on the measurable-cochains cohomology groups are Hausdorff.Comment: 52 pages. [Nov 22, 2011:] Major re-write with Calvin C. Moore as new co-author. Results from previous version strengthened and several new results added. [Nov 25, 2012:] Final version now available at springerlink.co

    Enhancing public awareness and promoting co-responsibility for marine litter in Europe: The challenge of MARLISCO

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    Marine litter is a pervasive and complex societal problem but has no simple solution. Inadequate practices at all levels of production–use–disposal contribute to accumulation of waste on land and at sea. Enhanced societal awareness but also co-responsibility across different sectors and improved interactions between stakeholders are necessary. MARLISCO was a European initiative, which developed and implemented activities across 15 countries. It worked towards raising societal awareness and engagement on marine litter, through a combination of approaches: public exhibitions in over 80 locations; a video competition involving 2100 students; and a legacy of educational and decision-supporting tools. 12 national participatory events designed to facilitate dialogue on solutions brought together 1500 stakeholders and revealed support for cross-cutting, preventive measures. Evaluation during implementation shows that these activities are effective in improving individuals' perceptions about the problem but also commitment in being part of the solution. This paper summarises MARLISCO's approach and highlights a selection of outcomes
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