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Cohomology of generalized configuration spaces.
- Source :
-
Compositio Mathematica . Feb2020, Vol. 156 Issue 2, p251-298. 48p. - Publication Year :
- 2020
-
Abstract
- Let $X$ be a topological space. We consider certain generalized configuration spaces of points on $X$ , obtained from the cartesian product $X^{n}$ by removing some intersections of diagonals. We give a systematic framework for studying the cohomology of such spaces using what we call 'twisted commutative dg algebra models' for the cochains on $X$. Suppose that $X$ is a 'nice' topological space, $R$ is any commutative ring, $H_{c}^{\bullet }(X,R)\rightarrow H^{\bullet }(X,R)$ is the zero map, and that $H_{c}^{\bullet }(X,R)$ is a projective $R$ -module. We prove that the compact support cohomology of any generalized configuration space of points on $X$ depends only on the graded $R$ -module $H_{c}^{\bullet }(X,R)$. This generalizes a theorem of Arabia. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0010437X
- Volume :
- 156
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Compositio Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 141343334
- Full Text :
- https://doi.org/10.1112/S0010437X19007747