On resolving singularities and relating bordism to homology

S. Buoncristiano; M. Dedò

Displaying similar documents to “On resolving singularities and relating bordism to homology”

Steenrod operations in subanalytic homology

Robert M. Hardt, Clint G. McCrory (1979)

Compositio Mathematica

Similarity:

On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles

Fouad Elzein, András Némethi (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Let $Y$ be a normal crossing divisor in the smooth complex projective algebraic variety $X$ and let $U$ be a tubular neighbourhood of $Y$ in $X$ . Using geometrical properties of different intersections of the irreducible components of $Y$ , and of the embedding $Y \subset X$ , we provide the “normal forms” of a set of geometrical cycles which generate $H_{*} (A, B)$ , where $(A, B)$ is one of the following pairs $(Y, \emptyset)$ , $(X, Y)$ , $(X, X - Y)$ , $(X - Y, \emptyset)$ and $(\partial U, \emptyset)$ . The construction is compatible with the weights in $H_{*} (A, B, ℚ)$ of Deligne’s mixed Hodge structure. The main technical...

Torsion in one-term distributive homology

Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra (2014)

Fundamenta Mathematicae

Similarity:

The one-term distributive homology was introduced in [Prz] as an atomic replacement of rack and quandle homology, which was first introduced and developed by Fenn-Rourke-Sanderson [FRS] and Carter-Kamada-Saito [CKS]. This homology was initially suspected to be torsion-free [Prz], but we show in this paper that the one-term homology of a finite spindle may have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their...

Foundations of Vietoris homology theory with applications to non-compact spaces

Robert E. Reed

Similarity:

CONTENTSPreface...................................................................................................................................... 5I. Introduction............................................................................................................................ 7II. Simple chains 2.1. Simplexes............................................................................................................ 12 2.2. Chains..............................................................................................................................

Duality theorems

W. Mayer (1948)

Fundamenta Mathematicae

Similarity:

Torsion in Khovanov homology of semi-adequate links

Józef H. Przytycki, Radmila Sazdanović (2014)

Fundamenta Mathematicae

Similarity:

The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ℤ₂-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs, which provides a link between link homology and the well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains ℤ₂-torsion if the corresponding Tait-type graph...

Bordism with codimension-one singularities

S. Buoncristiano, C. De Concini (1977)

Compositio Mathematica

Similarity:

Polynomials homologically supported on degeneracy loci

Piotr Pragacz, Jan Ratajski (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Hajime Sato (1972)

Annales de l'institut Fourier

Similarity:

We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold $M^{n}$ . The main theorem says that there is a unique obstruction element in $H_{n - 4} (M, ℋ^{3})$ , where $ℋ^{3}$ is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and $M$ is compact, we obtain a PL-manifold which is simple homotopy equivalent to $M$ .