相关论文: Absolute Poincar\'e duality in \'etale cohomology
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds,…
We investigate the rational cohomology of the quotient of (generalized) braid groups by the commutator subgroup of the pure braid groups. We provide a combinatorial description of it using isomorphism classes of certain families of graphs.…
We study a natural Hodge theoretic generalization of rational (or $\mathbb{Q}$-)homology manifolds through an invariant ${\rm HRH(Z)}$ where $Z$ is a complex algebraic variety. The defining property of this notion encodes the difference…
For a Poisson algebra $A$, by studying its universal enveloping algebra $A^{pe}$, we prove a duality theorem between Poisson homology and cohomology of $A$.
Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no…
For a finitely dominated Poincar\'e duality space $M$, we show how the author's total obstruction to the existence of a Poincar\'e embedding of the diagonal map $M \to M \times M$ relates to the Reidemeister trace of the identity map of…
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…
We continue our study on infinitesimal lifting properties of maps between locally noetherian formal schemes started in math.AG/0604241. In this paper, we focus on some properties which arise specifically in the formal context. In this vein,…
Frank Adams introduced the notion of a complex oriented cohomology theory represented by a commutative ring-spectrum and proved the Poincar\'e Duality theorem for this general case. In the current paper we consider oriented cohomology…
The well-known theory of Pontryagin duality provides a strong connection between the homology and cohomology theories of a profinite group in appropriate categories. A construction for taking the `profinite direct sum' of an infinite family…
Suppose M is a complex manifold of dimension $n+1$ and K is a hypersurface in M. By Poincar\'e duality we define a residue morphism $res:H^{k+1}(M\setminus K)\longrightarrow H_{2n-k}(K)$ which generalizes the classical Leray residue…
A general method for establishing results over a commutative complete intersection local ring by passing to differential graded modules over a graded exterior algebra is described. It is used to deduce, in a uniform way, results on the…
Banagl's method of intersection spaces allows to modify certain types of stratified pseudomanifolds near the singular set in such a way that the rational Betti numbers of the modified spaces satisfy generalized Poincar\'{e} duality in…
We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions where the terminal forms consist of isolated vertices. Our…
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…
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 theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincar\'e…
We present a geometric proof of the Poincar\'e-Dulac Normalization Theorem for analytic vector fields with singularities of Poincar\'e type. Our approach allows us to relate the size of the convergence domain of the linearizing…
Matlis duals of local cohomology modules are investigated with respect to many different topics (see section 0 - Introduction). One of these topics are complete intersections - see Corollary 1.1.4.
We introduce a structure termed ``connected cyclic diagonal'' on a chain complex, which induces stable power operations in its cohomology with the property that negative power operations consistently vanish. This chain level structure is…