Homotopy Gerstenhaber formality of Davis–Januszkiewicz spaces
| Autor: | Matthias O. Franz |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Ring (mathematics)
Pure mathematics Homotopy 010102 general mathematics Gerstenhaber algebra Structure (category theory) 16. Peace & justice Space (mathematics) Mathematics::Algebraic Topology 01 natural sciences Cohomology Mathematics (miscellaneous) 57S12 (Primary) 16E45 55P35 (Secondary) Mathematics::K-Theory and Homology Mathematics::Category Theory Differential graded algebra Loop space FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Mathematics |
| Zdroj: | Homology, Homotopy and Applications. 23:325-347 |
| ISSN: | 1532-0081 1532-0073 |
| DOI: | 10.4310/hha.2021.v23.n2.a17 |
| Popis: | A homotopy Gerstenhaber structure on a differential graded algebra is essentially a family of operations defining a multiplication on its bar construction. We prove that the normalized singular cochain algebra of a Davis-Januszkiewicz space is formal as a homotopy Gerstenhaber algebra, for any coefficient ring. This generalizes a recent result by the author about classifying spaces of tori and also strengthens the well-known dga formality result for Davis-Januszkiewicz spaces due to the author and Notbohm-Ray. As an application, we determine the cohomology rings of free and based loop spaces of Davis-Januszkiewicz spaces. 22 pages; conventions in Section 2.7 clarified, new Remark 3.2, minor changes |
| Databáze: | OpenAIRE |
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