We provide an explicit description of the Poincaré duals of each generator of the rational cohomology ring of the SU(2) character variety for a genus g surface with central extension — equivalently, ...that of the moduli space of stable holomorphic bundles of rank 2 and odd degree.
We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincaré duality in intersection (co)homology ...which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.
We extend the notion of Poincaré 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 general properties of equivariant
KK-theory for locally compact quantum groups, including the construction of exterior products. As an example, we prove that the standard Podleś sphere is equivariantly Poincaré dual to itself.
In a series of papers the authors introduced the so-called blown-up intersection cochains. These cochains are suitable to study products and cohomology operations of intersection cohomology of ...stratified spaces. The aim of this paper is to prove that the sheaf versions of the functors of blown-up intersection cochains are realizations of Deligne’s sheaves. This proves that Deligne’s sheaves can be incarnated at the level of complexes of sheaves by soft sheaves of perverse differential graded algebras. We also study Poincaré and Verdier dualities of blown-up intersections sheaves with the use of Borel–Moore chains of intersection.
In this paper we continue our investigations of 4-dimensional complexes in A. Cavicchioli, F. Hegenbarth, F. Spaggiari,
, Mediterr. J. Math.
(2020), 175. We study a class of finite oriented ...4-complexes which we call
-complexes, defined as follows. An
is a 4-dimensional finite oriented
-complex
with a single 4-cell such that
with a fundamental class
. By well-known results of Wall, any Poincaré complex is of this type. We are interested in two questions. First, for which 3-complexes
does an element
exist such that
is a Poincaré complex? Second, if there exists one, how many others can be constructed from
? The latter question was addressed studied in the above cited previous paper of the authors. In the present paper we deal with the first problem, and give necessary and sufficient conditions on
and
to satisfy Poincaré duality with
- and Λ-coefficients. Here Λ denotes the integral group ring of
. Before, we give a classification of all
-complexes based on the finite 3-complex
, and make some remarks concerning
- and Λ-Poincaré duality.
Abstract
The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a
generalized n
-manifold
X
n
, in order to ...produce an element of generalized homology theory, which is basic for calculations. In particular, we show how to construct an element of the
n
th Steenrod homology group
$H^{st}_{n} (X^{n}, \mathbb {L}^+)$
, where
+
is the connected covering spectrum of the periodic surgery spectrum , avoiding the use of the
geometric
splitting procedure, the use of which is standard in surgery on
topological
manifolds.
Mixed Weil cohomologies Cisinski, Denis-Charles; Déglise, Frédéric
Advances in mathematics (New York. 1965),
05/2012, Letnik:
230, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We define, for a regular scheme S and a given field of characteristic zero K, the notion of K-linear mixed Weil cohomology on smooth S-schemes by a simple set of properties, mainly: Nisnevich ...descent, homotopy invariance, stability (which means that the cohomology of Gm behaves correctly), and Künneth formula. We prove that any mixed Weil cohomology defined on smooth S-schemes induces a symmetric monoidal realization of some suitable triangulated category of motives over S to the derived category of the field K. This implies a finiteness theorem and a Poincaré duality theorem for such a cohomology with respect to smooth and projective S-schemes (which can be extended to smooth S-schemes when S is the spectrum of a perfect field). This formalism also provides a convenient tool to understand the comparison of such cohomology theories.
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