Related papers: On the various notions of Poincar\'e duality pair
We extend the notion of Poincar\'e duality in KK-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products. Along the way we discuss…
We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One…
We show that a RFRS Poincar\'e-duality group $G$ admits a virtual epimorphism to the integers whose kernel is itself a Poincar\'e-duality group over every field if and only if the $L^2$-homology of $G$ vanishes and so do the…
The well known Joker $\mathcal{A}(1)$-module of Adams and Priddy is known to be realisable as the cohomology of a $1$-connected space. By attaching an extra cell we obtain an $8$-dimensional Poincar\'e duality space whose mod~$2$ cohomology…
In the setting of global geometric Langlands, we show that miraculous duality on the stack of principal bundles on a curve intertwines the functor of Poincare series with the dual functor to Whittaker coefficients. We construct, for…
We extend the author's earlier computation and give coefficient formulas for the (quasimodular) Poincar\'e square series of weight 3/2 and weight 2 for the dual Weil representation for an even lattice.
I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the…
We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial…
In this paper, we discuss centroaffine geometry of polygons in $3$-space. For a polygon $X$ that is locally convex with respect to an origin together with a transversal vector field $U$, we define the centroaffine dual pair $(Y,V)$…
We characterize the real interpolation space between weighted $L^1$ and $W^{1,1}$ spaces on arbitrary domains different from $\mathbb{R}^n$, when the weights are positive powers of the distance to the boundary multiplied by an $A_1$ weight.…
This paper develops the study of Fox pairings of a group $G$ from the viewpoint of group cohomology. We compute some cohomology groups of Fox pairings of $G$, where $G$ admits a Poincar\'{e} duality group pair. We also suggest fundamental…
This paper extends the self-improvement result of Keith and Zhong in [16] to the two-measure case. Our main result shows that a two-measure $(p,p)$-Poincar\'e inequality for $1<p<\infty$ improves to a $(p,p-\varepsilon)$-Poincar\'e…
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary…
In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.
The tropical fundamental class of a rational balanced polyhedral fan induces cap products between tropical cohomology and tropical Borel-Moore homology. When all these cap products are isomorphisms, the fan is said to be a tropical…
This paper deals with fundamental properties of Poincar\'e half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincar\'e half-maps, their series expansions (Taylor and…
We adapt (over $\mathbb{F}_2$) the general notions of multiplicative function, Dirichlet convolution and Inverse. We get some interesting results, namely necessary conditions for an odd binary polynomial to be perfect. Note that we are…
A conjectural recursive relation for the Poincar\'e polynomial of the Hitchin moduli space is derived from wallcrossing in the refined local Donaldson-Thomas theory of a curve. A doubly refined generalization of this theory is also…
We prove some non-vanishing results of Hilbert Poincar\'e series. We derive these results, by showing that the Fourier coefficients of Hilbert Poincar\'e series satisfy some nice orthogonality relations for sufficiently large weight as well…
For any convex set $\Omega \subset {\mathbb R} ^N$, we provide a lower bound for the inverse of the Poincar\'e constant in $W ^ {1, 1}(\Omega)$: it refines an inequality in terms of the diameter due to Acosta-Duran, via the addition of an…