Multiplicative de Rham Theorems for Relative and Intersection Space Cohomology

Journal of Singularities
volume 19 (2019), 97-130

Received: 20 April 2018. Received in revised form: 7 August 2019.

DOI: 10.5427/jsing.2019.19g

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Abstract:

We construct an explicit de Rham isomorphism relating the cohomology rings of Banagl's de Rham and spatial approach to intersection space cohomology for stratified pseudomanifolds with isolated singularities. Intersection space (co-)homology is a modified (co-)homology theory extending Poincaré Duality to stratified pseudomanifolds. The novelty of our result compared to the de Rham isomorphism given previously by Banagl is, that we indeed have an isomorphism of rings and not just of graded vector spaces. We also provide a proof of the de Rham Theorem for cohomology rings of pairs of smooth manifolds which we use in the proof of our main result.

Keywords:

Singularity, Stratified Space, Pseudomanifold, Poincar\'e Duality, Intersection Space Cohomology, Intersection Cohomology, Sheaf Theory, De Rham Theorem, Relative De Rham Theorem, Differential Forms, Cellular Cup Products, Cup Products on Cochains

Mathematical Subject Classification (2010):

Primary: 55N33, 55N30, 14J17, 58A10, 58A12; secondary: 57P10, 81T3, 14J33

Author(s) information: