Homotopy diagrams of algebras

Markl, Martin

Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books, (2002), p. [161]-180 / Harvested from

Résumé

The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lect. Notes Math. 347, Springer-Verlag (1973; Zbl 0285.55012)] from topology to algebra.In topology the notion of operad extracts the essential algebraic information contained in the following example (endomorphism operad).The endomorphism operad $ℰ_{X}$ of a based space $X$ consists of the family $ℰ_{X} (j)$ $(j \geq 0)$ of spaces of based maps $X^{j} \to X$ , together with the collection of continuous maps $γ : ℰ_{X} (k) \times ℰ_{X} (j_{1}) \times \dots \times ℰ_{X} (j_{k}) \to ℰ_{X} (j)$ given by the formula $γ (f; g_{1}, \dots, g_{k}) = f (g_{1} \times \dots \times g_{k}),$ where $k, j_{1}, \dots, j_{k}, j$ are such that $j = \sum_{s = 1}^{k} j_{s}$ .Operads have proved to be a convenient tool to investigate, for example!

MR MR1972432 | Zbl 1024.55012

EUDML-ID : urn:eudml:doc:221412
Mots clés:

@article{701787,
     title = {Homotopy diagrams of algebras},
     booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2002},
     pages = {[161]-180},
     mrnumber = {MR1972432},
     zbl = {1024.55012},
     url = {http://dml.mathdoc.fr/item/701787}
}

Markl, Martin. Homotopy diagrams of algebras, dans Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books,  (2002), pp. [161]-180. http://gdmltest.u-ga.fr/item/701787/