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Proceedings/Recueil Des Communications Année : 2014

Algebra+Homotopy=Operad

Bruno Vallette

Résumé

This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher homotopies. We try to show how universal this theory is by giving many applications in Algebra, Geometry, Topology, and Mathematical Physics. (This text is accessible to any student knowing what tensor products, chain complexes, and categories are.)

Dates et versions

hal-00757010 , version 1 (25-11-2012)

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Bruno Vallette. Algebra+Homotopy=Operad. Cambridge Univ. Press. Hayashibara Forum Conference on Symplectic Geometry, Noncommutative Geometry and Physics, Berkeley, United States. 62, pp.229-290, 2014, Symplectic, Poisson, and noncommutative geometry, 978-1-107-05641-1. ⟨hal-00757010⟩
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