Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Discursive Control, Non-Domination and Hegelian Recognition Theory: Marrying Pettit’s Account(s) of Freedom with a Pippinian/Brandomian Reading of Hegelian Agency

The aim of this article is to combine Pettit’s account(s) of freedom, both his work on discursive control and on non-domination, with Pippin’s and Brandom’s reinterpretation of Hegelian rational agency and the role of recognition theory within it. The benefits of combining these two theories lie, as the article hopes to show, in three findings: first, re-examining Hegelian agency in the spirit of Brandom and Pippin in combination with Pettit’s views on freedom shows clearly why and in which way a Hegelian account of rational agency can ground an attractive socio-political account of freedom; second, the reconciling of discursive control and non-domination with Hegelian agency shows how the force and scope of recognition become finally tangible, without either falling into the trap of overburdening the concept, or merely reducing it to the idea of simple respect; third, the arguments from this article also highlight the importance of freedom as non-domination and how this notion is, indeed, as Pettit himself claims, an agency-freedom which aims at successfully securing the social, political, economic and even (some) psychological conditions for free and autonomous agency.

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

Finite domination and Novikov homology over strongly Z-graded rings

Let L be a unital Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent to a bounded complex of finitely generated projective L0-modules, generalising known results for twisted Laurent polynomial rings. The crucial hypothesis is that L is a strongly graded ring. 

Non-domination, non-alienation and social equality: towards a republican understanding of equality

The republican idea of non-domination stresses the importance of certain social relationships for a person’s freedom, showing that freedom is a social-relational state. While the idea of freedom as non-domination receives a lot of attention in the literature, republican theorists say surprisingly little about equality. Therefore, the aim of this paper is to carve out the contours of a republican conception of equality.. In so doing, I will argue that republican accounts of equality share a significant normative overlap with the idea of social equality. However, closer analysis of Philip Pettit’s account of ‘expressive egalitarianism’ (which Pettit sees as inherently connected to non-domination) and recent theories of social equality shows that republican non-domination – in contrast to what Pettit seems to claim – is not sufficient for securing (republican) social equality. In order to secure social equality for all, republicans would have to go beyond non-domination.

Civic Republicanism and Green Political Theory

Republicanism and in particular the civic republican tradition is not often one that one finds in discusions and debates within green political theory. It is interesting to note the relative lack of engagement between republican political theory and green political theory, unlike for example the research one can find on the relationship between green politics/political theory and liberalism, socialism and feminism. This is remarkable, given, as I hope to establish in this paper, the large areas of overlap between both, and in particular the compatibility of republican ideas and positions with key priciples and objectives of green theory, paricularly in relation to active citizenship, the centrality of recognising vulnerability and a commitment to liberty (as non-domination) and pluralism as key components of the transition to a more sustainable society.

Getting In and Getting On? The Experiences of Young People with Visual Impairments and Hearing Impairments in Third-Level Education

Young disabled people continue to be under-represented throughout further and higher education settings. Drawing on Pierre Bourdieu’s social theory of habitus, capital and field, this paper explores the practices of domination and oppression that have made it difficult for young people with visual impairments and hearing impairments to participate in third-level education on the same basis as non-disabled people. Twenty young people with hearing impairments and visual impairments were interviewed about their educational experiences. In addition, 31 interviews were conducted with third-level education providers, policy-makers and non-governmental organisations. This article has two aims: firstly, to critically examine the experiences of young people with hearing impairments and visual impairments in accessing and engaging with support provisions in further and higher education settings; and secondly, to identify and explore the diversity of ways in which these young people have managed and responded to the practices they have encountered. This article emphasises the journey from ability to dis-ability that young people with hearing and visual impairments experience in their quest for educational achievement. The ambiguities of “inclusion”, “widening participation” and “support” are highlighted and critiqued for their extensive failure to challenge taken-for-granted discourses.

Freedom, republicanism, and workplace democracy

This article explores the republican case for worker voice in economic enterprises based on the ideal of freedom as non-domination, and assesses its merits relative to two influential arguments for workplace democratization grounded on freedom understood as autonomy and self-determination. Two claims are advanced. The first is that the republican case for worker voice avoids difficulties associated with these two arguments. The second, however, is that the ideal of non-domination is insufficient, that an adequate understanding and defence of workplace democracy will also have to make significant reference to freedom understood as autonomy.

Teenagers' Perceptions and Experiences of Belfast as a Divided City

In this ‘research project’ case study, we provide an empirical example of how quantitative and qualitative methods were combined within a single study and discuss some of the strengths and weaknesses of our combined methodology which included questionnaires, photo-prompts and focus-group interviews. Our intention in using mixed methods was to enhance understandings of the meanings of space, place and territory on the everyday lives of young people growing up in Belfast. How do young people negotiate space in politically divided cities such as Belfast? Is territory important, and if so, why is it important? How do we construct an appropriate and relevant study design that can not only describe, but explain what place, space and territory mean to young people, and more importantly, how it impacts on their everyday lives? How useful is it to apply a mixed-methods approach to finding answers to these questions? We explain why and how we used a mixed-methods approach and illuminate some of the issues we encountered. We demonstrate how mixed methods can provide not just complementary but also new insights into the topic under investigation. We hope that the case study encourages you to experiment, or at least consider, the potential of using mixed methods.

Seasonal variation in dawn song characteristics in the common nightingale

Many male temperate zone passerines show a marked peak of singing activity before sunrise. The two main functions of this so-called dawn chorus are mate attraction and territory defence. We examined how seasonal patterns of different dawn song characteristics were related to mating status and to the breeding cycle of females in the common nightingale, Luscinia megarhynchos. We investigated two measures of song output: song rate and percentage performance time. We also calculated the proportion of 'whistle songs', a song category that is thought to be important in female choice. We predicted that if the main function of dawn singing in nightingales is to attract a social mate, then mated males should change their dawn singing behaviour after pair formation. In contrast, if dawn singing is mainly used in territory defence, we expected no difference in song traits between mated and unmated males throughout the season. We found that song rate and the proportion of whistle songs were low at the beginning of the season and did not predict future mating status. After arrival of females, all measures of dawn song performance remained largely constant throughout the breeding season, and we did not find significant differences in the seasonal variation between mated and unmated males. These findings are consistent with the hypothesis that song at dawn is important to defend a territory throughout the breeding season. (c) 2005 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.