LEADER 03404nam 2200457 450 001 9910793168103321 005 20211029205550.0 010 $a1-4704-4744-4 035 $a(CKB)4100000006516247 035 $a(MiAaPQ)EBC5501880 035 $a(RPAM)20632233 035 $a(PPN)230552609 035 $a(EXLCZ)994100000006516247 100 $a20180924d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntersection cohomology, simplicial blow-up and rational homotopy /$fDavid Chataur, Martintxo Saralegi-Aranguren, Daniel Tanre? 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2018. 215 $a1 online resource (122 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 254, Number 1214 311 $a1-4704-2887-3 320 $aIncludes bibliographical references and index. 327 $aSimplicial blow-up and intersection-cohomology -- Rational algebraic models -- Formality and examples. 330 $a"Let X be a pseudomanifold. In this text, we use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. We do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C.P. Rourke and B.J. Sanderson. We define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, we get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field Q. In a second step, we use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology. For that, we construct a functor from the category of filtered face sets to a category of perverse commutative differential graded Q-algebras (CDGA's) due to Hovey. We establish also the existence and uniqueness of a positively graded, minimal model of some perverse CDGA's, including the perverse forms over a filtered face set and their intersection cohomology. Finally, we prove the topological invariance of the minimal model of a PL-pseudomanifold whose regular part is connected, and this theory creates new topological invariants. This point of view brings a definition of formality in the intersection setting and examples are given. In particular, we show that any nodal hypersurface in CP(4), is intersection-formal"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 254, Number 1214. 606 $aIntersection homology theory 615 0$aIntersection homology theory. 676 $a514.23 700 $aChataur$b David$f1974-$01482600 702 $aSaralegi-Aranguren$b Martintxo$f1960- 702 $aTanre?$b Daniel 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793168103321 996 $aIntersection cohomology, simplicial blow-up and rational homotopy$93700326 997 $aUNINA