On the rational homotopy type of intersection spaces

• Verfasst von: Wrazidlo, Dominik [VerfasserIn]
• Titel: On the rational homotopy type of intersection spaces
• Verf.angabe: Dominik Wrazidlo
• Jahr: 2020
• Umfang: 23 S.
• Teil: volume:20
• Teil: year:2020
• Teil: pages:251-273
• Teil: extent:23
• Fussnoten: Gesehen am 23.06.2021
• Titel Quelle: Enthalten in: Journal of Singularities
• Ort Quelle: Cambridge, Mass. : Worldwide Center of Mathematics, 2010
• Jahr Quelle: 2020
• Band/Heft Quelle: 20(2020), Seite 251-273
• ISSN Quelle: 1949-2006
• DOI: doi:10.5427/jsing.2020.20k
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1761088815

Abstract

Banagl's method of intersection spaces allows modification of certain types of stratified pseudomanifolds near the singular set in such a way that the rational Betti numbers of the modified spaces satisfy generalized Poincaré duality in analogy with Goresky-MacPherson's intersection homology. In the case of one isolated singularity, we show that the duality isomorphism comes from a nondegenerate intersection pairing which depends on the choice of a chain representative of the fundamental class of the regular stratum. On the technical side, we use piecewise linear polynomial differential forms due to Sullivan to define a suitable commutative cochain algebra model for intersection spaces. We show that the weak equivalence class of our model does not depend on choices, which implies uniqueness of the rational intersection space cohomology ring. Our construction parallels Banagl's commutative cochain algebra of smooth differential forms modeling intersection space cohomology, and we show that both algebras are weakly equivalent.