Maps between 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...

0 the Homology of Iterated Loop Spaces

Maps between Classifying Spaces

In 1976, Adams & Mahmud 3] published the rst systematic study of the problem of determining the homological properties of maps between classifying spaces of compact connected Lie groups. This was continued in later work by one or both authors: Adams 2] extended some of the results to the case of non-connected Lie groups by using complex K-theory; while Adams & Mahmud 4] identiied further restri...

Complete maps of molecular-loop conformational spaces

This paper presents a numerical method to compute all possible conformations of distance-constrained molecular loops, i.e., loops where some interatomic distances are held fixed, while others can vary. The method is general (it can be applied to single or multiple intermingled loops of arbitrary topology) and complete (it isolates all solutions, even if they form positive-dimensional sets). Gen...

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 ...