(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably. We in particular show that the fusion bases of the (2+1)-dimensional theory lead to a rich set of bases for the (3+1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian. Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.Comment: 27 pages, many figures, v2: minor correction

in defense of a presuppositional account of slurs

Abstract In the last fifteen years philosophers and linguists have turned their attention to slurs: derogatory expressions that target certain groups on the basis of race, gender, sexual orientation, nationality and so on. This interest is due to the fact that, on the one hand, slurs possess puzzling linguistic properties; on the other hand, the questions they pose are related to other crucial issues, such as the descriptivism/expressivism divide, the semantics/pragmatics divide and, generally speaking, the theory of meaning. Despite these recent investigations about pejoratives, there is no widely accepted explanation of slurs:in my paper I consider the intuitions we have about slurs and I assess the difficulties that the main theories encounter in explaining how these terms work in order to identify the phenomena that a satisfactory account of slurs needs to explain. Then, I focus on the pragmatic theories that deal with the notions of conventional implicature and pragmatic presupposition: I assess the objections that have been raised and I propose two ways of defending the presuppositional account, taking into consideration the notion of cancellability. I will claim that the reason why most pragmatic strategies seem to fail to account for slurs is that they assume a rigid divide between conventional implicatures and presuppositions that should not be taken for granted. Reconsidering the relationship between these two notions gives a hint about how a pragmatic account of slurs should look like. Finally, I assess the problem of which presupposition slurs in fact trigger

Reanalyzing Chisholm Paradox. Structural Insights

In this paper I focus on the conditions that have to be met for Chisholm’s Paradox (CP) to occur. My claim is that identity and structure are notions closely related to each other. I propose a discussion in which the minimal framework for CP is set, then analyze the paradox in terms of S5, and suggest that in order to capture the core of the paradox one should use a dynamic valuation function for the model. Identity appears, at this point, to be dependent upon a structuralist point of vie

A family of varieties with exactly one pointless rational fiber

We construct a concrete example of a 1-parameter family of smooth projective geometrically integral varieties over an open subscheme of P^1_Q such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.Comment: 4 pages. Some stylistic changes, replaced an argument in Lemma 3.1 with a simpler argument as suggested by the referee. To appear in J. Th\'eor. Nombres Bordeau

Transcendental Brauer elements via descent on elliptic surfaces

Transcendental Brauer elements are notoriously difficult to compute. Work of Wittenberg, and later, Ieronymou, gives a method for computing 2-torsion transcendental classes on surfaces that have a genus 1 fibration with rational 2-torsion in the Jacobian fibration. We use ideas from a descent paper of Poonen and Schaefer to remove this assumption on the rational 2-torsion.Comment: 10 pages, small edits made to the introduction, references added in the introductio