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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...
Autores principales: | , , |
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Lenguaje: | eng |
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American Mathematical Society
2018
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Acceso en línea: | http://cds.cern.ch/record/2648159 |
_version_ | 1780960645622005760 |
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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. |
id | cern-2648159 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2018 |
publisher | American Mathematical Society |
record_format | invenio |
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 |