String topology of classifying spaces

Chataur, David; Menichi, Luc

doi:10.1515/crelle.2011.140

Cited by 27 publications

(63 citation statements)

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“…In, 6 Chateur and Menichi proved that when taken with coefficients in a field the homology of LBG is a co-unital non unital homological conformal field theory, and the cohomology H * (LBG) is a Batalin-Vilkovisky algebra structure. In particular they give another way to describe the product on H * (LBG).…”

Section: String Topology Of Point Orbifoldsmentioning

confidence: 99%

A Survey on Orbifold String Topology

Ángel¹

2013

Geometric, Algebraic and Topological Methods for Quantum Field Theory

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The aim of this short communication is to review some classical results on string topology of manifolds and discuss recent extensions of this theory to orbifolds. In particular, we review the relation between the loop homology of the classiying space of the orbifold and the Hochschild cohomology of dg-ring naturally associated to the orbifold. IntroductionString topology is the study of the topological properties of to the space of smooth loops LM on a closed and oriented manifold M . In particular algebraic structures defined on the homology of the loop space. The area started with the paper 5 by Chas and Sullivan where they defined an intersection product in the homology of the free loop spacehaving total degree −n.Orbifolds, originally known as V -manifolds by I. Satake, 18 and named this way by W. Thurston, 19 are a generalizations of manifolds, locally they look like the quotient of euclidean space by the action of a finite group. They appear naturally in many areas such as moduli problems, noncommutative geometry and topology. It is natural to ask, What is the string topology of an orbifold? In this survey article we give different answers in the case where the orbifold is a global quotient.The character of this paper is expository and is organized as follows. In section one we review some of the classical theory for manifolds, and state Geometric, Algebraic and Topological Methods for Quantum Field Theory Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/22/15. For personal use only. 332 A. Angelthe results of Chas-Sullivan 5 and Cohen-Jones 7 on the string topology of manifolds. In section two we discuss the necessary background on orbifolds. In section three, we review the construction of 14 of the string topology of quotient orbifolds over the rationals and the construction of 3 of the string topology of quotient orbifolds over the integers. In section four we specialize to the case of [ * /G] and give geometric descriptions of the string topology product on the cohomology H * (LBG). Acknowledgements

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Section: String Topology Of Point Orbifoldsmentioning

confidence: 99%

A Survey on Orbifold String Topology

Ángel¹

2013

Geometric, Algebraic and Topological Methods for Quantum Field Theory

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“…In [7], Chataur and the author, and in [1], Behrend, Ginot, Noohi and Xu developed a string topology theory dual to Chas-Sullivan string topology. Property 57.…”

Section: String Topology Of Classifying Spacesmentioning

confidence: 99%

“…where the right triangle is the triangle considered in the proof of Theorem 54 of [7] and the left square is induced by the commutative square of topological spaces …”

mentioning

confidence: 99%

Van den Bergh isomorphisms in string topology

Menichi¹

2010

J. Noncommut. Geom.

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“…Dans un premier temps (section 2), nous établirons une description du dual du loop produit pour un espace de Gorenstein de dimension formelle n en termes de modèles de Sullivan (cf. [5,2,6]). Ensuite (section 3), nous donnerons le modèle minimal de Sullivan de l'espace E Γ lorsque M est un espace homogène G/H via une action de Γ sur le groupe de Lie compacte connexe G et finalement (section 3), nous indiquerons un exemple avec une action de Γ = S 1 sur G = U (n + 1) dépendant d'un paramètre λ = 0, 1.…”

Section: Introductionunclassified

Produit de Chas–Sullivan et actions d'un groupe de Lie connexe

Mbiakop

2015

Comptes Rendus. Mathématique

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String topology of classifying spaces

Cited by 27 publications

References 35 publications

A Survey on Orbifold String Topology

A Survey on Orbifold String Topology

Van den Bergh isomorphisms in string topology

Produit de Chas–Sullivan et actions d'un groupe de Lie connexe

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