Cohomology of generalized configuration spaces
| Autor: | Dan Petersen |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Zero (complex analysis) Geometric Topology (math.GT) K-Theory and Homology (math.KT) Cohomology with compact support Commutative ring Topological space Cartesian product 01 natural sciences Cohomology Mathematics - Geometric Topology symbols.namesake Mathematics - K-Theory and Homology 0103 physical sciences FOS: Mathematics symbols Algebraic Topology (math.AT) Mathematics - Algebraic Topology 010307 mathematical physics Configuration space 0101 mathematics Commutative property Mathematics |
| Zdroj: | Compositio Mathematica |
| ISSN: | 1570-5846 0010-437X |
| DOI: | 10.1112/s0010437x19007747 |
| Popis: | 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 "tcdga models" for the cochains on $X$. We prove the following theorem: suppose that $X$ is a "nice" topological space, $R$ is any commutative ring, $H^\bullet_c(X,R)\to H^\bullet(X,R)$ is the zero map, and that $H^\bullet_c(X,R)$ is a projective $R$-module. Then the compact support cohomology of any generalized configuration space of points on $X$ depends only on the graded $R$-module $H^\bullet_c(X,R)$. This generalizes a theorem of Arabia. 47 pages. V2: significant revision, inaccuracies corrected. Final version |
| Databáze: | OpenAIRE |
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