Homotopy transfer and rational models for mapping spaces
| Autor: | Urtzi Buijs, Javier J. Gutiérrez |
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| Rok vydání: | 2016 |
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Context (language use)
Type (model theory) Mathematics::Algebraic Topology 01 natural sciences Combinatorics Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology Algebra en Topologie 0101 mathematics Mathematics Algebra and Topology Algebra and Number Theory Functional analysis 55P62 (Primary) 54C35 (Secondary) Rational homotopy theory Homotopy 010102 general mathematics Mathematics::Rings and Algebras Order (ring theory) Nilpotent Number theory ComputingMethodologies_DOCUMENTANDTEXTPROCESSING 010307 mathematical physics Geometry and Topology |
| Zdroj: | Journal of Homotopy and Related Structures, 11, 2, pp. 309-332 Journal of Homotopy and Related Structures, 11, 309-332 |
| ISSN: | 2193-8407 |
| DOI: | 10.1007/s40062-015-0107-x |
| Popis: | By using homotopy transfer techniques in the context of rational homotopy theory, we show that if $C$ is a coalgebra model of a space $X$, then the $A_\infty$-coalgebra structure in $H_*(X;\mathbb{Q})\cong H_*(C)$ induced by the higher Massey coproducts provides the construction of the Quillen minimal model of $X$. We also describe an explicit $L_\infty$-structure on the complex of linear maps ${\rm Hom}(H_*(X; \mathbb{Q}), \pi_*(\Omega Y)\otimes\mathbb{Q})$, where $X$ is a finite nilpotent CW-complex and $Y$ is a nilpotent CW-complex of finite type, modeling the rational homotopy type of the mapping space ${\rm map}(X, Y)$. As an application we give conditions on the source and target in order to detect rational $H$-space structures on the components. Comment: 21 pages. Final version. To appear in J. Homotopy Relat. Struct |
| Databáze: | OpenAIRE |
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