Related papers: Poincare Duality Pairs in Dimension Three

In this paper, we show that the twisted Poincar\'e duality between Poisson homology and cohomology can be derived from the Serre invertible bimodule. This gives another definition of a unimodular Poisson algebra in terms of its Poisson…

The space of polynomial differential equations of a fixed degree with a center singularity has many irreducible components. We prove that pull back differential equations form an irreducible component of such a space. The method used in…

We establish a partial extension of the Poincar\'e duality theorem of Jell-Rau-Shaw to tropical hypersurfaces arising from non-primitive triangulations. We introduce a notion of level of primitivity for triangulations of lattice polytopes…

We define a space of relative embedded thickenings of a given map from a finite complex to a Poincare Duality space, and show that there is a highly connected stabilization map between such spaces induced by fiberwise suspension. As a…

According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters providing the right sides of the differential…

We study geometric characterizations of the Poincar\'{e} inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of…

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

We investigate Poincar\'e series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms…

We investigate the properties of pure derived categories of module categories, and show that pure derived categories share many nice properties of classical derived categories. In particular, we show that bounded pure derived categories can…

Poincar{\'e} and Sobolev inequalities for differential forms on Heisenberg balls, involving Rumin's differentials, are given. Furthermore, a global homotopy of Rumin's complex which improves differentiability of Rumin forms is provided on…

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate…

In this paper we prove Poincar\'e inequalities for the Discrete de Rham (DDR) sequence on a general connected polyhedral domain $\Omega$ of $\mathbb{R}^3$. We unify the ideas behind the inequalities for all three operators in the sequence,…

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…

In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely…

In a recent collaboration, Hiroki Matsui and the author introduced a new proof of the reconstruction theorem of Bondal-Orlov and Ballard, using Matsui's construction of a ringed space associated to a triangulated category. This paper first…

In this paper, we construct a functorial quantization of (co)Poisson Hopf algebras within a broad categorical framework. We further introduce categories naturally associated with (co)Poisson Hopf algebras, namely Drinfeld-Yetter modules.…

The unimodularity condition for a Poisson structure (ie., a Poisson structure with a trivial modular class) induces a Poincar\'e duality between its Poisson homology and its Poisson cohomology. Therefore an information about the Poisson…

Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular on the complex plane). A…

The kappa-deformed dual pair of Poincare algebra and Poincare group is formulated in the framework of Heisenberg doubles. The covariant kappa-deformed phase space is described in detail as a subalgebra.The realizations of proposed algebraic…