cam a22 4 4500 528739425 CHVBK 20201023213247.0 180921t20182018riua b||| 001 0 eng|d 978-1-4704-2887-7 1-4704-2887-3 (NEBIS)011266838 (RERO)R008841088 (OCoLC)1048614044 AAA fre SzZuIDS NEBIS EPF-BIB rda QA3 .A57 no.1214 QA612.32 .C48 2018 s1ma rero 514/.23 23 Chataur David 1974- (DE-588)1165661004 auteur aut Intersection cohomology, simplicial blow-up and rational homotopy David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré Providence, Rhode Island American Mathematical Society [2018] ©2018 viii, 108 pages illustrations 25 cm Memoirs of the American Mathematical Society number 1214 1214 (NEBIS)000023178 574068856 Includes bibliographical references (pages 103-105) and index Simplicial blow-up and intersection-cohomology -- Rational algebraic models -- Formality and examples "Let X be a pseudomanifold. In this text, we 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. We 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. We 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, we 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 Q. In a second step, we use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology. For that, we construct a functor from the category of filtered face sets to a category of perverse commutative differential graded Q-algebras (CDGA's) due to Hovey. We establish also the existence and uniqueness of a positively graded, minimal model of some perverse CDGA's, including the perverse forms over a filtered face set and their intersection cohomology. Finally, we prove the topological invariance of the minimal model of a PL-pseudomanifold whose regular part is connected, and this theory creates new topological invariants. This point of view brings a definition of formality in the intersection setting and examples are given. In particular, we show that any nodal hypersurface in CP(4), is intersection-formal"-- Homotopy theory Topological spaces HOMOLOGIEGRUPPEN + KOHOMOLOGIEGRUPPEN (ALGEBRAISCHE TOPOLOGIE) ger (ETHUDK)000013046 ethudk HOMOTOPIETHEORIE (ALGEBRAISCHE TOPOLOGIE) ger (ETHUDK)000013065 ethudk SCHNITT-THEORIE (ALGEBRAISCHE GEOMETRIE) ger (ETHUDK)000012814 ethudk TOPOLOGISCHE INVARIANTEN ger (ETHUDK)000013033 ethudk Intersection homology theory Homologie d'intersection (RERO)A021134701 rero u HOMOLOGIEGRUPPEN + KOHOMOLOGIEGRUPPEN (ALGEBRAISCHE TOPOLOGIE) ger 515.142.21 nebis E1 u SCHNITT-THEORIE (ALGEBRAISCHE GEOMETRIE) ger 512.734.2 nebis E1 u HOMOTOPIETHEORIE (ALGEBRAISCHE TOPOLOGIE) ger 515.143 nebis E1 u TOPOLOGISCHE INVARIANTEN ger 515.127 nebis E1 u GROUPES D'HOMOLOGIE + GROUPES DE COHOMOLOGIE (TOPOLOGIE ALGÉBRIQUE) fre 515.142.21 nebis E1 u HOMOLOGY GROUPS + COHOMOLOGY GROUPS (ALGEBRAIC TOPOLOGY) eng 515.142.21 nebis E1 u INTERSECTION THEORY (ALGEBRAIC GEOMETRY) eng 512.734.2 nebis E1 u THÉORIE DE L'INTERSECTION (GÉOMÉTRIE ALGÉBRIQUE) fre 512.734.2 nebis E1 u THÉORIE DE L'HOMOTOPIE (TOPOLOGIE ALGÉBRIQUE) fre 515.143 nebis E1 u HOMOTOPY THEORY (ALGEBRAIC TOPOLOGY) eng 515.143 nebis E1 u TOPOLOGICAL INVARIANTS eng 515.127 nebis E1 u INVARIANTS TOPOLOGIQUES fre 515.127 nebis E1 rero ams 55 rero ams 57 Saralegi-Aranguren Martintxo auteur aut Tanré Daniel auteur aut Memoirs of the American Mathematical Society 1214 BK020000 XK020000 XK020000 E64-20181002 nebis EN E02120 E02-20180829 122 E01-20180926 E64S E64-20181002 RERO RE61011 RE61011 RE610110001 55/422 NEBIS E64 E64 E64BI S 24.1214 NEBIS E01 E01 MG P 711653: 1214 NEBIS E02 E02 E02RB 57 CHA NEBIS 100 1- Chataur David 1974- (DE-588)1165661004 auteur aut NEBIS 490 0- Memoirs of the American Mathematical Society number 1214 1214 (NEBIS)000023178 574068856 NEBIS 700 1- Saralegi-Aranguren Martintxo auteur aut NEBIS 700 1- Tanré Daniel auteur aut RERO 100 1- Chataur David 1974- (IDREF)06106680X cre RERO 490 1- Memoirs of the American Mathematical Society 1214 RERO 700 1- Saralegi-Aranguren Martintxo 1960- (IDREF)229891365 RERO 700 1- Tanré Daniel (IDREF)031658083 RERO 830 -- Memoirs of the American Mathematical Society 1214 NEBIS EAD50 EBI01 E01 https://opac.nebis.ch/objects/pdf03/e01_978-1-4704-2887-7_01.pdf Titelblatt und Inhaltsverzeichnis VIEW pdf