Related papers: Poincare Duality Pairs in Dimension Three

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…

We obtain an explicit formula for the Poincare duality isomorphism H^{n-3}(Mbar(ell)) to Z/2 for the space of isometry classes of n-gons with specified side lengths, if ell is monogenic in the sense of Hausmann-Rodriguez. This has potential…

We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincar\'e…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

We describe an application of Poincar\'e duality for completed homology spaces (as defined by Emerton) to level raising for p-adic modular forms. This allows us to give a new description of the image of Chenevier's p-adic Jacquet-Langlands…

Let f: P-->W be an embedding of a compact polyhedron in a closed oriented manifold W, let T be a regular neighborhood of P in W and let C:=closure(W-T) be its complement. Then W is the homotopy push-out of a diagram C<--dT-->P. This…

Non-trivial extensions of the three dimensional Poincar\'e algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three dimensional generalizations of fractional supersymmetry of order…

We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincar\'{e} duality complexes in which a loop of a product…

We investigate the problem of Poincar\'e duality for $L^p$ differential forms on bounded subanalytic submanifolds of $\mathbb{R}^n$ (not necessarily compact). We show that, when $p$ is sufficiently close to $1$ then the $L^p$ cohomology of…

The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and…

In this article we define a Poincare series on a subspace of a complex analytic germ, induced by a multi-index filtration on the ambient space. We compute this Poincare series for subspaces defined by principal ideals. For plane curve…

We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.

In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geometric applications of the orientability. In particular, a…

Let $\mathscr{C}$ be a $2$-Calabi-Yau triangulated category with two cluster tilting subcategories $\mathscr{T}$ and $\mathscr{U}$. Results by Demonet-Iyama-Jasso and J{\o}rgensen-Yakimov known as tropical duality says that the index with…

We discuss Poincar\'e duality complexes X and the question whether or not their Spivak normal fibration admits a reduction to a vector bundle in the case where the dimension of X is at most 4. We show that in dimensions less than 4 such a…

We prove a version of Poincar\'e's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced. The theorem may have a wide range of applications and can…

Using the general theory of [10] ( hep-th 9412058 ), quantum Poincar\'e groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most…

We construct periodic families of Poincare complexes, partially solving a question of Hodgson that was posed in the proceedings of the 1982 Northwestern homotopy theory conference. We also construct infinite families of Poincare complexes…

This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate…

We exhibit a Poisson module restoring a twisted Poincare duality between Poisson homology and cohomology for the polynomial algebra R=C[X_1,...,X_n] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This…