Related papers: Poincare duality in dimension 3
In this paper we address the relation between the orbifold fundamental group and the topology of the underlying space. In particular, under the assumption that the orbifold fundamental group is equal to the fundamental group of the…
We study the link between a compact hypersurface in $\P^{n+1}$ and the set of all its tangent planes. In this context, we identify $\P^{n+1}$ to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise…
The Poincare conjecture is analyzed in the context of Calabi-Yau $n$-folds. A simple treatment is given by embedding the three-manifolds into these CY manifolds, and then taking the orbifold limit. The higher-dimensional proofs are also…
Let M be a Poincare duality space of dimension at least four. In this paper we describe a complete obstruction to realizing the diagonal map M -> M x M by a Poincare embedding. The obstruction group depends only on the fundamental group and…
In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted…
For the infinite-dimensional extension of the Dirichlet distribution, the super Poincare inequality does not hold based on the result in [14], so we establish the weighted super Poincare inequalities for this measure with respect to two…
We explore the constraints imposed by Poincar\'e duality on the resonance varieties of a graded algebra. For a 3-dimensional Poincar\'e duality algebra $A$, we obtain a fairly precise geometric description of the resonance varieties…
This is the extended write-up of a series of lectures on the duality between the Sine-Gordon model and the Thirring model. Prepared for the London Theory Institute (LonTI) - Fall 2022: a PhD-level mini-course, with exercises and a guide to…
Lectures on Poincare invariant quantum theory presented at TJNAF.
We extend Poincar\'e duality in \'etale cohomology from smooth schemes to regular ones. This is achieved via a formalism of trace maps for local complete intersection morphisms.
A generic massive Thirring Model in three space-time dimensions exhibits a correspondence with a topologically massive bosonized gauge action associated to a self-duality constraint, and we write down a general expression for this…
This review paper deals with dimension theory of polynomial rings over certain families of pullbacks. While the literature is plentiful, this field is still developing and many contexts are yet to be explored. I will thus restrict the scope…
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant…
In this paper I review the theoretical progresses in studying the diffractive DIS in the colour--dipole approach.
Let M be a simply-connected closed Poincare Duality complex of dimension n. Then M is obtained by attaching a cell of highest dimension to its (n-1)-skeleton M'. Conditions are given for when the skeletal inclusion i:M' --> M has the…
The Chouinard's formula for injective dimension is extended to the Gorenstein injective dimension.
We expand on the recent derivation of 3d dualities using bosonization. We present in some detail a general class of Abelian duals.
We use dual graphs and generating sequences of valuations to compute the Poincare series of non-divisorial valuations on function fields of dimension two. The Poincare series are shown to reflect data from the dual graphs and hence carry…
We present a complete solution of the constraints for three-dimensional N=2 conformal supergravity in terms of unconstrained prepotentials. This allows us to develop a prepotential description of the off-shell versions of N=2 Poincare and…
We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincar\'e duality between their generalized persistence diagrams. A heavy…