## A CHEN MODEL FOR MAPPING SPACES AND THE SURFACE PRODUCT (905)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Ginot905achen,

author = {Grégory Ginot and Thomas Tradler and Mahmoud Zeinalian},

title = {A CHEN MODEL FOR MAPPING SPACES AND THE SURFACE PRODUCT},

year = {905}

}

### OpenURL

### Abstract

Abstract. We develop a machinery of Chen iterated integrals for higher Hochschild complexes which are complexes whose differentials are modeled by an arbitrary simplicial set much in the same way that the ordinary Hochschild differential is modeled by 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, which is an analogue of the loop product in string topology. As an application we show that this product is homotopy invariant. We prove Hochschild-Kostant-Rosenberg type theorems and use them to give explicit formulae for the surface product of odd spheres and Lie groups. Contents

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Citation Context ...M)) is the dual of the map δ g,h .44 G. GINOT, T. TRADLER, AND M. ZEINALIAN We now want to dualize the Hochschild cup product for surfaces. Since M is a Poincaré duality space, by the main result of =-=[LS]-=-, there exists a differential graded commutative algebra (A, d), weakly equivalent to (Ω•M, ddR), which is simply connected, finite dimensional and is equipped with a trace Adim(M) ǫ → R such that: • ... |