David Chataur
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View article: Relation between intersection homology and homotopy groups
Relation between intersection homology and homotopy groups Open
As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which Gajer associates to a…
View article: Homotopy truncations of homotopically stratified spaces
Homotopy truncations of homotopically stratified spaces Open
Intersection homology of Goresky and MacPherson can be defined from the\nDeligne sheaf, obtained from truncations of complexes of sheaves. As\nintersection homology is not the homology of a particular space, the search for\na family of spa…
View article: Homotopy truncations of homotopically stratified spaces
Homotopy truncations of homotopically stratified spaces Open
Intersection homology of Goresky and MacPherson can be defined from the Deligne sheaf, obtained from truncations of complexes of sheaves. As intersection homology is not the homology of a particular space, the search for a family of spaces…
View article: Perverse homotopy groups
Perverse homotopy groups Open
As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates t…
View article: Relation between intersection homology and homotopy groups
Relation between intersection homology and homotopy groups Open
As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates t…
View article: SIMPLICIAL INTERSECTION HOMOLOGY REVISITED
SIMPLICIAL INTERSECTION HOMOLOGY REVISITED Open
Intersection homology is defined for simplicial, singular and PL chains. In the case of a filtered simplicial complex, it is well known that the three versions are isomorphic. This isomorphism is established by using the PL case as an inte…
View article: Simplicial intersection homology revisited
Simplicial intersection homology revisited Open
Intersection homology is defined for simplicial, singular and PL chains and it is well known that the three versions are isomorphic for a full filtered simplicial complex. In the literature, the isomorphism, between the singular and the si…
View article: Natural operations in Intersection Cohomology
Natural operations in Intersection Cohomology Open
Eilenberg-MacLane spaces, that classify the singular cohomology groups of topological spaces, admit natural constructions in the framework of simplicial sets. The existence of similar spaces for the intersection cohomology groups of a stra…
View article: Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces Open
We describe the E-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its E-…
View article: Blown-up intersection cochains and Deligne's sheaves
Blown-up intersection cochains and Deligne's sheaves Open
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…
View article: Blown-up intersection cohomology
Blown-up intersection cohomology Open
In previous works, we have introduced the blown-up intersection cohomology\nand used it to extend Sullivan's minimal models theory to the framework of\npseudomanifolds, and to give a positive answer to a conjecture of M. Goresky\nand W. Pa…
View article: Singular decompositions of a cap product
Singular decompositions of a cap product Open
In the case of a compact orientable pseudomanifold, a well-known theorem of M. Goresky and R. MacPherson says that the cap product with a fundamental class factorizes through the intersection homology groups. In this work, we show that thi…
View article: Rational homotopy of complex projective varieties with normal isolated singularities
Rational homotopy of complex projective varieties with normal isolated singularities Open
Let X be a complex projective variety of dimension n with only isolated normal singularities. In this paper, we prove, using mixed Hodge theory, that if the link of each singular point of X is (n-2) ${(n-2)}$ -connected, then X is a formal…
View article: Mixed Hodge structures on the intersection homotopy type of complex varieties with isolated singularities
Mixed Hodge structures on the intersection homotopy type of complex varieties with isolated singularities Open
A homotopical treatment of intersection cohomology recently developed by Chataur-Saralegui-Tanré associates a "perverse algebraic model" to every topological pseudomanifold, extending Sullivan's presentation of rational homotopy to interse…
View article: Mixed Hodge structures on the intersection homotopy type of complex\n varieties with isolated singularities
Mixed Hodge structures on the intersection homotopy type of complex\n varieties with isolated singularities Open
A homotopical treatment of intersection cohomology recently developed by\nChataur-Saralegui-Tanr\\'e associates a "perverse algebraic model" to every\ntopological pseudomanifold, extending Sullivan's presentation of rational\nhomotopy to i…
View article: Intersection Homology. General perversities and topological invariance
Intersection Homology. General perversities and topological invariance Open
Topological invariance of the intersection homology of a pseudomanifold without codimension one strata, proven by Goresky and MacPherson, is one of the main features of this homology. This property is true for codimension-dependent pervers…
View article: Intersection Homology. General perversities and topological invariance
Intersection Homology. General perversities and topological invariance Open
Topological invariance of the intersection homology of a pseudomanifold without codimension one strata, proven by Goresky and MacPherson, is one of the main features of this homology. This property is true for codimension-dependent pervers…