Tetrahedra on deformed spheres and integral group cohomology.
The braid groups of the projective plane.
The geometry of configuration spaces for closed chains in two and three dimensions.
The integral cohomology algebras of ordered configuration spaces of spheres.
The rational homotopy type of configuration spaces of two points
We prove that the rational homotopy type of the configuration space of two points in a -connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.
The Salvetti complex and the little cubes
For a real central arrangement , Salvetti introduced a construction of a finite complex Sal which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement , the Salvetti complex Sal serves as a good combinatorial model for the homotopy type of the configuration space of points in , which is homotopy equivalent to the space of k little -cubes. Motivated by the importance of little cubes in homotopy theory, especially in the study of...
The space of clouds in Euclidean space.
The space of intervals in a Euclidean space.
Topological Order Complexes and Resolutions of Discriminant Sets
Topological order complexes and resolutions of discriminant sets.
Torus actions, equivariant moment-angle complexes, and coordinate-subspace arrangements.