Displaying similar documents to “On the cohomology algebra of a fiber.”

Homotopy algebras via resolutions of operads

Markl, Martin

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Summary: All algebraic objects in this note will be considered over a fixed field k of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over k . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [, “La renaissance des opérads”, Sémin. Bourbaki 1994/95, Exp. No....

Deformations of Batalin-Vilkovisky algebras

Olga Kravchenko (2000)

Banach Center Publications

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We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a Gerstenhaber (Lie) algebra structure on A, an operator of an order higher than 2 (Koszul-Akman definition) leads to the structure of a strongly homotopy Lie algebra ( L ∞ -algebra) on A. This allows us to give a definition of a Batalin-Vilkovisky algebra up to homotopy. We also make a conjecture...

Homotopy diagrams of algebras

Markl, Martin

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The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [ and , 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...