## The symmetrisation of n-operads and compactification of real configuration spaces

Venue: | Adv. Math |

Citations: | 15 - 3 self |

### BibTeX

@ARTICLE{Batanin_thesymmetrisation,

author = {M. A. Batanin},

title = {The symmetrisation of n-operads and compactification of real configuration spaces},

journal = {Adv. Math},

year = {},

pages = {684--725}

}

### Years of Citing Articles

### OpenURL

### Abstract

It is well known that the forgetful functor from symmetric operads to nonsymmetric operads has a left adjoint Sym1 given by product with the symmetric group operad. It is also well known that this functor does not affect the category of algebras of the operad. From the point of view of the author’s theory of higher operads, the nonsymmmetric operads are 1-operads and Sym1 is the first term of the infinite series of left adjoint functors Symn, called symmetrisation functors, from n-operads to symmetric operads with the property that the category of one object, one arrow,..., one (n − 1)-arrow algebras of an n-operad A is isomorphic to the category of algebras of Symn(A). In this paper we consider some geometrical and homotopical aspects of the symmetrisation of n-operads. We follow Getzler and Jones and consider their decomposition of the Fulton-Macpherson operad of compactified real configuration spaces. We construct an n-operadic counterpart of