Iterated wreath product of the simplex category and iterated loop spaces

Iterated Wreath Product of the Simplex Category and Iterated Loop Spaces

Generalising Segal’s approach to 1-fold loop spaces, the homotopy theory of n-fold loop spaces is shown to be equivalent to the homotopy theory of reduced Θn-spaces, where Θn is an iterated wreath-product of the simplex category ∆. A sequence of functors from Θn to Γ allows for an alternative description of the Segal-spectrum associated to a Γ-space. In particular, each Eilenberg-MacLane space ...

Iterated integrals and the loop product

The purpose of this paper is to describe string topology from the viewpoint of Chen’s iterated integrals. Let M be a compact closed oriented d-manifold and LM be the free loop space of M , the set of unbased smooth maps from S to M . Let H∗(LM) be the homology of the free loop space shifted by the dimension of the manifold i.e. H∗(LM) = H∗+d(LM). Chas and Sullivan found the product on H∗(LM) wh...

0 the Homology of Iterated Loop Spaces

Loop Spaces and Iterated Higher Dimensional Enrichment

There is an ongoing massive effort by many researchers to link category theory and geometry, especially homotopy coherence and categorical coherence. This constitutes just a part of the broad undertaking known as categorification as described by Baez and Dolan. This effort has as a partial goal that of understanding the categories and functors that correspond to loop spaces and their associated...

Iterated Loop Algebras

Iterated loop algebras are by definition obtained by repeatedly applying the loop construction, familiar from the theory of affine Kac-Moody Lie algebras, to a given base algebra. Our interest in this iterated construction is motivated by its use in the realization of extended affine Lie algebras, but the construction also appears naturally in the study of other classes of algebras. This paper ...