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We establish a Kauffman–Murasugi–Thistlethwaite-type theorem for alternating knots in a solid torus. Specifically, we show that any dotted-reduced alternating diagram of a knot in a handlebody realises the minimal crossing number. The proof relies on a generalisation of the Jones polynomial to the setting of handlebodies. A stronger version of this result was already proved by Boden et al. [‘Adequate links in thickened surfaces and the generalized Tait conjectures’, Algebr. Geom. Topol.23(5) (2023), 2271–2308] using a different generalised Jones polynomial; this paper largely expands on one of the main proof tools.
Transforming Conflict examines lessons learned from the Northern Ireland and Border Counties conflict transformation process through social and economic development and their consequent impacts and implications for practice and policymaking, with a range of functional recommendations produced for other regions emerging from and seeking to transform violent conflict. It provides, for the first time, a comprehensive assessment of the region’s transformation activity, largely amongst grassroots actors, enabled by a number of specific funding programmes, namely the International Fund for Ireland, Peace I and II and INTERREG I, II and IIIA. These programmes have facilitated conflict transformation over more than two decades, presenting a case ripe for lesson sharing. In focusing on the politics of the socioeconomic activities that underpinned the elite negotiations of the peace process, key theoretical transformation concepts are firstly explored, followed by an examination of the social and economic context of Northern Ireland and the Border Counties. The three programmes and their impacts are then assessed before considering what policy lessons can be learned and what recommendations can be made for practice. This is underpinned by a range of semi-structured interviews and the author’s own experience as a project promoter through these programmes in the Border Counties for more than a decade.
This chapter is structured into three sections: lessons learned from each of the three programmes; implications for conflict transformation practice in terms of a lack of specialist knowledge and understanding, non-existent (government) conflict transformation policy and a strategic conflict transformation planning deficit; recommendations for transformation practice. It notes that the assessment of some of these programmes has delivered some stark insights: conflict is a costly experience - transforming a violent and conflict ridden society into one that allows societal structures and levels to peacefully co-exist is a complex, multi-faceted and long-term task. Therefore, the key questions asked and answered by this chapter are what lessons have been learned from these programmes? What are the implications of these lessons for those charged with implementing and managing conflict transformation processes? What recommendations can be made to other societies emerging from conflict, seeking the successful and sustainable transformation of their conflicts? In making recommendations for transformation practice and policy, it is acknowledged that they are not of the ‘one cap fits all’ variety. Nevertheless, most of these proposals are fundamental to successful conflict transformation taking place and need to be carefully considered by those in a position to do so.
This chapter provides an outline description of the three funding programmes in terms of their background, their management and administrative structures and the types of activities they funded. Of the three conflict transformation programmes (tools) which Northern Ireland and the Border Counties have benefited from, two of them, the IFI and the Peace programmes, were specifically tailored for the region. Together with the INTERREG I, II and III(A) programmes, they have directly contributed over €3.25billion to the region since 1986. While intricate in their make-up, they illustrate a fine line between standard socioeconomic activities and those aimed at transforming conflict. Effectively analysing their impact on the region’s conflict transformation process necessitates comprehending their complex backgrounds, administrative structures and activities, a complexity which largely increased rather than decreased as they progressed.
This chapter examines Northern Ireland and the Border Counties from a social and economic development perspective - some understanding of this and the extent of its contributory role in the conflict is deemed useful in understanding social and economic development (and the progress made by the three programmes) as a transforming factor. Social and economic development is also at the heart of the three transformation tools, suggesting that deprivation, poverty and social exclusion are viewed by the EU and the Irish and British governments as part of the conflict’s legacy. With the normalisation of politics in Northern Ireland, the economy has begun to take centre stage indicating the transformation process as a whole will not succeed without a specific concentration on this area. A key consideration is whether the ongoing transformation process has made any substantial difference to the social and economic lives of the peoples of this region. A very brief overview of the conflict from 1600 until the ceasefires in 1994 is provided, followed by an examination of the effects of the conflict on the region’s social and economic development in terms of the economy, unemployment, educational disadvantage and poverty and social exclusion.
This chapter critically examines the impacts the three funding programmes have had on the region’s conflict transformation process. Some have been positive, having supported thousands of projects. However, a weak aspect has been the limited attention and funding for social development, preferring instead that which is easier to account for – concrete visuals or fixed funding amounts for formal projects over set periods, underpinning a top-down, funder-focused approach to evaluation. It assesses the extent of their effectiveness in transforming the conflict firstly through general observations provided largely in terms of strengths and weaknesses and secondly by assessing the impact of each programme against the five hypotheses developed in Chapter 2: an attempt has been made to address the root causes of the conflict thus bringing about substantial changes in the social and economic structures of society; vertical and horizontal capacity has been developed and integrated through the involvement of all levels of society in the transformation process thus enabling the empowerment of the society’s citizens; a long-term view has been taken of the transformation process; the tools used were tailored to suit the particular situation thus facilitating peacebuilding rather than imposing or dictating terms; the tools have not done any harm.
The introduction highlights how conflict transformation is a largely misunderstood concept within the broadly defined field of conflict management and how transformation through social and economic development is even less understood, reflected in the theoretical and practitioner discourse. The chapter is therefore concerned with providing greater conceptual and theoretical clarification, while seeking to examine the practical and policy lessons from the Northern Ireland and Border Counties case study and their consequent impacts and implications for practice, with the aim of making a number of practice and policy recommendations for other regions emerging from violent conflict. In the context of this case study, it introduces a number of conflict transformation funding programmes which have been operating in this region since 1986, facilitating transformation specifically through social and economic development: the International Fund for Ireland, Peace I, II and III and INTERREG I, II and IIIA. They have been responsible for a huge increase in practice, particularly at the grassroots level, prompting previously unforeseen levels of citizen empowerment and local ownership of the peace process. Having enabled significant levels of learning to take place, they provide a suitable context for exploring conflict transformation in action, presenting a case ripe for lesson sharing.
The conclusion returns to the conceptual and theoretical examination outlined in Chapter 2 which initially informed and shaped the book’s assessment, Lederach’s exploration of the interdependence, justice and process-structure gaps, to assess the extent to which they have been narrowed by the three programmes examined. While the middle-range is certainly critical to sustaining change, this book has also found that the nature of the three programmes ensured the valuable capacity existing within the grassroots was as equally instrumental as that of the middle level in delivering and sustaining conflict transformation, particularly when the political failed, clearly demonstrating the intrinsic importance of participative democracy to representative democracy. Because of the practice perspective of this book, the conclusion acknowledges the need to marry the theoretical to the practical. It challenges governments to take up the recommendations, cognisant that this is a considerable challenge: as today’s world faces growing social and economic conflict, building peace without the inclusion of social and economic development in the conflict transformation matrix as a strand of the web as necessary as the political, cultural, spiritual or psychological, will be devastating.