“All that ‘needs’ stuff… It’s just me!”: Contesting, navigating and satisfying needs in a homelessness hostel setting

People who are homeless are frequently discussed in relation to the complex needs that they present with, given their experiences of overlapping physical and mental ill-health, substance use and childhood trauma. This thesis critically examines the ways that needs fit alongside the context of homelessness, the nature of such needs and how they play out. The research question at the heart of this study is ‘how are needs understood (contested), negotiated (navigated) and supported (satisfied) for people who are homeless’. A single-site instrumental case study was undertaken at a 50-bed complex needs hostel in an English city over 22 days in a 4-month period. The study was informed by a conceptual framework linking Stockwell’s ‘unpopular groups’, Honneth’s ‘recognition’ theory and Fricker’s ‘epistemic injustice’. Data collection was undertaken through semi-structured interviews with the residents (n=28) and staff (n=25), structured observations of handover meetings (n=25), team meetings (n=4) and keywork meetings (n=13) and documentary analysis of agency policies and other relevant documents (n=20). The results identify that the liminal nature of the hostel policies, geographies, homelessness experience and staff working conditions shaped how needs were understood. The study also found that needs included functional, relational, ontological and safety or safeguarding needs but there were tensions in how each type were navigated. Encounters with external professionals were pivotal in the satisfaction of needs but could be based on limited understanding, uncaring attitudes, and power dynamics. These findings can be analytically generalised to inform broader policy, practice, and research. The study challenges assumptions about the inherent complexity and hierarchical nature of the needs of people who are homeless. The study also identifies barriers to the acceptance of need by professionals and considers the impact this has on residents’ expressions of their own needs. Concerns about the inversion of professional responses are noted, where wellbeing and care are proposed as core to the offer of support but very little of this care is experienced by people who are homeless. The thesis makes an important contribution to the understanding of needs of people who are homeless at a time when rough sleeping is growing, and hostels are coming under scrutiny in terms of their outcomes for residents with complex needs

The critical group of a combinatorial map

Motivated by the appearance of embeddings in the theory of chip-firing and the critical group of a graph, we introduce a version of the critical group (or sandpile group) for combinatorial maps, that is, for graphs embedded in orientable surfaces. We provide several definitions of our critical group, by approaching it through analogues of the cycle--cocycle matrix, the Laplacian matrix, and as the group of critical states of a chip-firing game (or sandpile model) on the edges of a map.Our group can be regarded as a perturbation of the classical critical group of its underlying graph by topological information, and it agrees with the classical critical group in the plane case. Its cardinality is equal to the number of spanning quasi-trees in a connected map, just as the cardinality of the classical critical group is equal to the number of spanning trees of a connected graph.Our approach exploits the properties of principally unimodular matrices and the methods of delta-matroid theory