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A Chen model for mapping spaces and the surface product

Grégory Ginot, Thomas Tradler, Mahmoud Zeinalian (2010)

Annales scientifiques de l'École Normale Supérieure

We develop a machinery of Chen iterated integrals for higher Hochschild complexes. These are complexes whose differentials are modeled on an arbitrary simplicial set much in the same way the ordinary Hochschild differential is modeled on the circle. We use these to give algebraic models for general mapping spaces and define and study the surface product operation on the homology of mapping spaces of surfaces of all genera into a manifold. This is an analogue of the loop product in string topology....

A formula for the rational LS-category of certain spaces

Luis Lechuga, Aniceto Murillo (2002)

Annales de l’institut Fourier

In this paper we find a formula for the rational LS-category of certain elliptic spaces which generalizes or complements previous work of the subject. This formula is given in terms of the minimal model of the space.

A G -minimal model for principal G -bundles

Shrawan Kumar (1982)

Annales de l'institut Fourier

Sullivan associated a uniquely determined D G A | Q to any simply connected simplicial complex E . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space E . In case E is the total space of a principal G -bundle, ( G is a compact connected Lie-group) we associate a G -equivariant model U G [ E ] , which is a collection of “ G -homotopic” D G A ’s | R with G -action. U G [ E ] will, in general, be different from the Sullivan’s minimal model of the space E . U G [ E ] contains the total rational...

A Note on Hamiltonian Lie Group Actions and Massey Products

Zofia Stępień, Aleksy Tralle (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that the property of having only vanishing triple Massey products in equivariant cohomology is inherited by the set of fixed points of hamiltonian circle actions on closed symplectic manifolds. This result can be considered in a more general context of characterizing homotopic properties of Lie group actions. In particular it can be viewed as a partial answer to a question posed by Allday and Puppe about finding conditions ensuring the "formality" of G-actions.

Axiome du cube et foncteurs de Quillen

Jean-Pierre Doeraene, Daniel Tanré (1995)

Annales de l'institut Fourier

Les approches de Whitehead et de Ganea, conceptuellement différentes, permettent toutes deux la définition de la catégorie de Lusternik et Schnirelmann. Le premier auteur a montré qu’elles existent dans le cadre des catégories à modèles de Quillen et qu’elles coïncident lorsqu’est vérifié un axiome supplémentaire non autodual, l’axiome du cube. Nous étendons ici cette étude au cadre de catégories à modèles non nécessairement propres et ne vérifiant pas l’axiome du cube. Pour cela, l’hypothèse globale...

Basic constructions in rational homotopy theory of function spaces

Urtzi Buijs, Aniceto Murillo (2006)

Annales de l’institut Fourier

Via the Bousfield-Gugenheim realization functor, and starting from the Brown-Szczarba model of a function space, we give a functorial framework to describe basic objects and maps concerning the rational homotopy type of function spaces and its path components.

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Luc Menichi (2009)

Bulletin de la Société Mathématique de France

Let M be any compact simply-connected oriented d -dimensional smooth manifold and let 𝔽 be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of M , H H * ( S * ( M ) , S * ( M ) ) , extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjectured to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on M , H * + d ( L M ) introduced by Chas and Sullivan. We also show that the negative cyclic cohomology H C - * ( S * ( M ) ) ...

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