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Intersection cohomology, simplicial blow-up and rational homotopy

Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a f...

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Autores principales: Chataur, David, Saralegi-Aranguren, Martintxo, Tanré, Daniel
Lenguaje:eng
Publicado: American Mathematical Society 2018
Materias:
Acceso en línea:http://cds.cern.ch/record/2648159
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author Chataur, David
Saralegi-Aranguren, Martintxo
Tanré, Daniel
author_facet Chataur, David
Saralegi-Aranguren, Martintxo
Tanré, Daniel
author_sort Chataur, David
collection CERN
description Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field \mathbb Q. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.
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spelling cern-26481592021-04-21T18:39:48Zhttp://cds.cern.ch/record/2648159engChataur, DavidSaralegi-Aranguren, MartintxoTanré, DanielIntersection cohomology, simplicial blow-up and rational homotopyMathematical Physics and MathematicsLet X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field \mathbb Q. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.American Mathematical Societyoai:cds.cern.ch:26481592018
spellingShingle Mathematical Physics and Mathematics
Chataur, David
Saralegi-Aranguren, Martintxo
Tanré, Daniel
Intersection cohomology, simplicial blow-up and rational homotopy
title Intersection cohomology, simplicial blow-up and rational homotopy
title_full Intersection cohomology, simplicial blow-up and rational homotopy
title_fullStr Intersection cohomology, simplicial blow-up and rational homotopy
title_full_unstemmed Intersection cohomology, simplicial blow-up and rational homotopy
title_short Intersection cohomology, simplicial blow-up and rational homotopy
title_sort intersection cohomology, simplicial blow-up and rational homotopy
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2648159
work_keys_str_mv AT chataurdavid intersectioncohomologysimplicialblowupandrationalhomotopy
AT saralegiarangurenmartintxo intersectioncohomologysimplicialblowupandrationalhomotopy
AT tanredaniel intersectioncohomologysimplicialblowupandrationalhomotopy