Related papers: Spanning via Cech Cohomology
We compute the \v{C}ech cohomology ring of a countable product of infinite projective spaces, and that of an infinite flag manifold. The method of our first result in fact computes the cohomology ring of a countably infinite product of…
One of the advantages of working with Alexander-Spanier-\v{C}ech type cohomology theory is the continuity property: For inverse systems of sufficiently well-behaved spaces, the result of taking the cohomology of their limit is a direct…
The homology of an unknown subspace of Euclidean space can be determined from the intrinsic \v{C}ech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace $X$ of…
A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is…
Let $M$ be a compact, unit volume, Riemannian manifold with boundary. In this paper we study the homology of a random \v{C}ech-complex generated by a homogeneous Poisson process in $M$. Our main results are two asymptotic threshold…
We consider a Plateau problem in codimension $1$ in the non-parametric setting. A Dirichlet boundary datum is given only on part of the boundary $\partial \Omega$ of a bounded convex domain $\Omega\subset\mathbb{R}^2$. Where the Dirichlet…
The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the…
Plateau's problem is not a single conjecture or theorem, but rather an abstract framework, encompassing a number of different problems in several related areas of mathematics. In its most general form, Plateau's problem is to find an…
Constraint satisfaction (CSP) and structure isomorphism (SI) are among the most well-studied computational problems in Computer Science. While neither problem is thought to be in $\texttt{PTIME},$ much work is done on $\texttt{PTIME}$…
Selective segmentation involves incorporating user input to partition an image into foreground and background, by discriminating between objects of a similar type. Typically, such methods involve introducing additional constraints to…
Image segmentation refers to the process to divide an image into nonoverlapping meaningful regions according to human perception, which has become a classic topic since the early ages of computer vision. A lot of research has been conducted…
We compute the cohomology of polygon spaces using their identification to (semi) stable configuration of weighted points on complex projective line. This cohomology is already given by J.C.Hausmann and A. Knutson but we use a different…
Bounded cohomology of groups was first defined by Johnson and Trauber during the seventies in the context of Banach algebras. As an independent and very active research field, however, bounded cohomology started to develop in 1982, thanks…
Scene labeling is the problem of assigning an object label to each pixel. It unifies the image segmentation and object recognition problems. The importance of using contextual information in scene labeling frameworks has been widely…
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directions. First, we find bounds on the…
The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…
In this paper the cosheaf homology is investigated from different viewpoints: the behavior under site morphisms, connections with Cech homology via spectral sequences, and description of cosheaf homology using hypercoverings. It is proved…
In a previous joint work with Aurichi and Magalh\~aes Jr., we showed that the topological spaces arising from the edge-end structure of infinite graphs define a proper subfamily of those obtained through the well-known (vertex-)ends. This…
M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula to make selections among singular simplexes. This formula needs a notion of dimension for…
In this survey paper, we present \v{C}ech and sheaf cohomologies -- themes that were presented by Koszul in University of S\~ao Paulo during his visit in the late 1950s -- we present expansions for categories of generalized sheaves (i.e,…