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The Salvetti complex and the little cubes

Dai Tamaki (2012)

Journal of the European Mathematical Society

For a real central arrangement 𝒜 , Salvetti introduced a construction of a finite complex Sal ( 𝒜 ) which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement 𝒜 k - 1 , the Salvetti complex Sal ( 𝒜 k - 1 ) serves as a good combinatorial model for the homotopy type of the configuration space F ( ℂ , k ) of k points in C , which is homotopy equivalent to the space C 2 ( k ) of k little 2 -cubes. Motivated by the importance of little cubes in homotopy theory, especially in the study of...

The top cohomology class of certain spaces.

Aniceto Murillo (1991)

Extracta Mathematicae

In this abstract we present an explicit formula for a cycle representing the top class of certain elliptic spaces, including the homogeneous spaces. For thet, we shall rely on the connection between Sullivan's theory of minimal models and Rational homotopy theory for which [3], [6] and [10] are standard references.

The Vietoris system in strong shape and strong homology

Bernd Günther (1992)

Fundamenta Mathematicae

We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology.

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