On the cohomology algebra of a fiber.

Menichi, Luc

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

Homotopy algebras via resolutions of operads

Markl, Martin

Similarity:

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

Similarity:

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 ( $L_{\infty}$ -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

Similarity:

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...

Homotopy Lie algebras; lower central series and the Koszul property.

Papadima, Stefan, Suciu, Alexander I. (2004)

Geometry & Topology

Similarity:

The Milnor-Moore theorem in Tame Homotopy theory.

Hans Scheerer, Daniel Tanré (1991)

Manuscripta mathematica

Similarity:

The double bar and cobar constructions

H. J. Baues (1981)

Compositio Mathematica

Similarity:

Hopf algebras up to homotopy and the Bockstein spectral sequence.

Scott, Jonathan (2005)

Algebraic & Geometric Topology

Similarity:

The Hochschild cohomology of a closed manifold

Yves Felix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2004)

Publications Mathématiques de l'IHÉS

Similarity:

Let M be a closed orientable manifold of dimension and $𝒞^{*} (M)$ be the usual cochain algebra on M with coefficients in a field. The Hochschild cohomology of M, $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is a graded commutative and associative algebra. The augmentation map $ε : 𝒞^{*} (M) \to 𝑘$ induces a morphism of algebras $I : H H^{*} (𝒞^{*} (M); 𝒞^{*} (M)) \to H H^{*} (𝒞^{*} (M); 𝑘)$ . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of $H H^{*} (𝒞^{*} (M); 𝑘)$ , which is in general quite small. The algebra $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is expected to...