Intersection Cohomology, Simplicial Blow-Up and Rational Homotopy - Couverture souple

Chataur, David; Saralegi-Aranguren, Martintxo; Longo, Roberto; Weiner, Mihaly

Couverture souple

ISBN 10 : 1470428873 ISBN 13 : 9781470428877

Editeur : American Mathematical Society, 2018

Synopsis

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1470428873
• ISBN 13: 9781470428877
• Reliure: Broché
• Nombre de pages: 108
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible