This thesis proposes an improved notion of coefficient system for Lagrangian Floer Homology which allows one to produce nontrivial invariants away from characteristic 2, even when coherent orientations of moduli spaces of Floer trajectories do not exist. This explains a suggestion of Witten. The invariant can be computed in examples, and the method explained below should be extensible to other Floer-theoretic invariants. The basic idea is that the moduli spaces of curves admit fundamental classes in homology with coefficients in the orientation lines of the moduli spaces, and the usual construction of coherent orientations actually shows that these fundamental classes naturally map to spaces of paths twisted with appropriate coefficient systems. These twisted path spaces admit enough algebraic structure to make sense of Floer homology with coefficients in these path spaces.

<p>Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological stability for the homology of the unordered configuration spaces of a connected manifold. The main difficulty is the case that the manifold is compact because there are no obvious maps inducing stability and the homology eventually is periodic instead of stable. We resolve this issue by constructing a new chain-level stabilization map for configuration spaces.</p>

archives@tulane.edu / There is a deep analogy between the theory of covering spaces and the theory offield extensions. Indeed, for many theorems about the Galois groups of field extensionsthere are analogous statements for the fundamental groups of covering spaces. Thepurpose of this thesis is to present an expository account of the connections betweenthese two useful concepts of algebra and geometry. / 1 / Dejun Zhang

A. Z. Petrov gave a complete list of all local group actions on a four-dimensional space-time that admit an invariant Lorentz metric, up to an equivalence relation. His list was compiled by directly constructing all possible Lie algebras of infinitesimal generators of group actions that preserve a Lorentz metric. The goal of this paper was to verify that classification by algebraically constructing a list of all possible three-dimensional homogeneous spaces and calculating which among them have a non-degenerate invariant metric.

This study investigates creating antiracist spaces and determining what an antiracist sociohistorical geography looks like. I argue that an antiracist sociohistorical geography is always necessarily unfinished and in a state of becoming. I introduce as my study site a section of Toronto, Ontario, Canada, that was once a neighbourhood known as The Ward. At different times in the past, the land of this area was home to the Mississauga of the Credit First Nation, a Black community, a Jewish community, and a Chinese community. Through investigations of these historic racialized communities and through field site examination, I first document how current cultural representations within this space create racist exclusions. Next, through discussion of my experience with the Ontario Black History Society’s (OBHS) walking tour in and around this space, and through analysis of one-on-one interviews with OBHS representatives, I show the tour as creating starting points for developing antiracist geographies. Finally, by imagining the space devoid of racist exclusions, I illustrate what an antiracist sociohistorical geography might look like but also that the portrayal is a spatial and temporal moment and therefore unfinished. I combine an anti-essentialist antiracist historical methodology with critical discourse analysis and critical ethnography. My main finding is that inclusions of excluded racialized groups into dominant discourse can contribute to naming and perhaps troubling particular racisms, but do not automatically disrupt systems and structures that (re)create exclusions. To deconstruct these powers, antiracism must incorporate ongoing disruptions of dominance over space. My study shows the potential for shifting discursive meanings around racialized bodies in relation to each other and sociohistorical geographies they occupy. These shifts have implications for how sociohistorical spaces become forums of social studies and history education in everyday spaces and in schools, as people (re)learn to read bodies within sociohistorical spaces in antiracist ways.

No description available.

No description available.

No description available.

For my thesis project, I have chosen to explore the exaptation of a vacant office building doomed to be demolished in Stockholm into a residential tower. This project’s focus is the investigation of the reusability of our existing built environment in a sustainable way together with diverse collective living concepts and a comparison of the value added from a deconstruction, reuse and an environmentally sound concept versus a full demolition and subsequent new construction.The paramount challenges we are facing are the changing climate and limitation of natural resources. We have to address this issue by rethinking our societal and habitational models; the way we live, how we inhabit space, how do we use resources and consume goods and especially how do we design and build our cities.

No / Tranquility has a number of facets. Given the role that tranquility plays in societies, it is increasingly seen as an environmental indicator. Earlier, some have identified tranquility as contributing to health and wellbeing of individuals and the society, making it to be rooted in the context of sound natural ecosystems as a desirable environmental characteristic. Previous studies have identified tranquility places as having links to nature and natural features, wild landscapes, naturally behaving wildlife and natural sounds. The question of how tranquility can be evaluated and the perception of tranquility by visitors is a continuous recurrence. This study therefore selected seven green open spaces in Hong Kong in an attempt to answer these and other questions that are arising. Although results vary, it however provides a perspective on how people perceive tranquil spaces as part of their leisure and recreation indulgence, given rise to the concept of eco-leisure. / Research Grants Council of the Hong Kong Special Administrative Region, China (RGC/GRF, CUHK449612)