Related papers: Pseudocycles for Borel-Moore Homology

We introduce the notion of locally consistent system of half-spaces for a real hyperplane arrangement. We embed a sphere in the complexified complement by shifting the real unit sphere into the imaginary direction indicated by the…

As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…

In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…

Matchbox manifolds are foliated spaces with totally disconnected transversals. Two matchbox manifolds which are homeomorphic have return equivalent dynamics, so that invariants of return equivalence can be applied to distinguish…

Given a semipositive symplectic manifold, we prove that the pseudocycle genus-zero Gromov-Witten invariants are equal to the polyfold genus-zero Gromov-Witten invariants.

Pseudo-cones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counterpart to convex bodies containing the origin in the…

We define families of invariants for elements of the mapping class group of S, a compact orientable surface. Fix any characteristic subgroup H of pi_1(S) and restrict to J(H), any subgroup of mapping classes that induce the identity modulo…

We introduce a sheaf-theoretic approach to tropical homology, especially for tropical homology with potentially non-compact supports. Our setup is suited to study the functorial properties of tropical homology, and we show that it behaves…

Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…

We investigate the surjectivity of the real cycle class map from $I$-cohomology to classical intergral cohomology for some real smooth varieties, in particular surfaces. This might be considered as one of several possible incarnations of…

We describe polar homology groups for complex manifolds. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincare residue…

As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into…

We study the Duflot filtration on the Borel equivariant cohomology of smooth manifolds with a smooth $p$-torus action. We axiomatize the filtration and prove analog of several structural results about equivariant cohomology rings in this…

A stratified pseudomanifold is normal if its links are connected. A normalization of a stratified pseudomanifold $X$ is a normal stratified pseudomanifold $Y$ together with a finite-to-one projection $n:Y\to X$ satisfying a local condition…

We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We give ncecessary and sufficient conditions for a function defined on the union of the Torelli groups to be an…

In this paper we give a geometric construction of the Borel equivariant (co)homology for spaces with a $G$-action, where $G$ is a compact Lie group with the property that the adjoint representation is orientable. A nice feature of these…

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…

In this paper we study pseudoholomorphic curves with brake symmetry in symplectization of a closed contact manifold. We introduce the pseudoholomorphic curve with brake symmetry and the corresponding moduli space. Then we get the virtual…

Poincare duality lies at the heart of the homological theory of manifolds. In the presence of the action of a group it is well-known that Poincare duality fails in Bredon's ordinary, integer-graded equivariant homology. We give here a…

When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…