Configuration spaces of tori

Twisted cohomology of configuration spaces of the plane and spaces of maximal tori via point-counting

We consider two families of algebraic varieties Yn indexed by natural numbers n: the configuration space of unordered n-tuples of distinct points on C, and the space of unordered n-tuples of linearly independent lines in C. Let Wn be any sequence of virtual Sn-representations given by a character polynomial, we compute H(Yn;Wn) for all i and all n in terms of double generating functions. One co...

Configuration Spaces

0 7 4 0 7 4 5 9 / 0 4 / $ 2 0 . 0 0 © 2 0 0 4 I E E E distributed systems is most often specified in terms of quality-of-service (QoS) requirements, which help define the acceptable levels of dependability with which capabilities such as processing capacity, data throughput, or service availability reach users. For longer-term properties such as scalability, maintainability, adaptability, and s...

On Embeddings of Tori in Euclidean Spaces

Configuration Spaces of Linkages

This paper studies the configuration space of all possible positions of a linkage in R n. For example, it shows that for every compact algebraic set, there is a linkage whose configuration space is analytically isomorphic to a finite number of copies of the algebraic set. If flexible edges are allowed, any compact set given by polynomial equalities and inequalities is the configuration space of...

On Loop Spaces of Configuration Spaces

This article gives an analysis of topological and homological properties for loop spaces of configuration spaces. The main topological results are given by certain choices of product decompositions of these spaces, as well as “twistings” between the factors. The main homological results are given in terms of extensions of the “infinitesimal braid relations” or “universal YangBaxter Lie relations”.