Related papers: Poincare duality quivers
The aim of this note is to prove the analogue of Poincar\'e duality in the chiral Hodge cohomology.
Using methods of KK-theory, we generalize Poincare duality to the framework of twisted K-theory.
We study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal)…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
An proof of Poincare Duality with local coefficients and with compact support is provided. The proof does not require Sheaf Theory or anything equivalent and is thus more accessible for the general audience.
We discuss the consequences of the Poincar\'e duality, versus AS- Gorenstein property, for Koszul algebras (homogeneous and non homogeneous). For homogeneous Koszul algebras, the Poincar\'e duality property implies the existence of twisted…
This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.
The full duality between the $\kappa$-Poincar\'e algebra and $\kappa$-Poincar\'e group is proved.
We discuss the notion of Poincar\'e duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincar\'e duality is pointed out for the existence of twisted potentials…
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
We derive and discuss the constraints induced by Poincare' invariance on the form of the heavy-quark potential up to order 1/m^2. We present two derivations: one uses general arguments directly based on the Poincare' algebra and the other…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
We establish a number of foundational results on Poincar\'e spaces which result in several applications. One application settles an old conjecture of C.T.C. Wall in the affirmative. Another result shows that for any natural number n, there…
We prove a twisted Poincar\'e duality for (full) Hopf algebroids with bijective antipode. As an application, we recover the Hochschild twisted Poincar\'e duality of Van Den Bergh [VDB]. We also get a Poisson twisted Poincar\'e duality,…
We investigate some connections between two different ways of defining Poincar\'e Duality, and relate them geometrically to the level curve mapping.
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…
For the chiral QCD_2 on a cylinder, we give a construction of a quantum theory consistent with anomaly. We construct the algebra of the Poincare generators and show that it differs from the Poincare one.
We make explicit Poincar\'{e} duality for the equivariant $K$-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the $K$-theory orientation.
In a previous paper, math.AT/0304079, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincare duality space, each component of the Auslander-Reiten quiver is isomorphic to…
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…