Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...

Sierpinski space Ω is injective in the category Top of topological spaces, but not in any of the larger cartesian closed categories Conv of convergence spaces and Equ of equilogical spaces. We show that this negative result extends to all sub-cccs of Equ and Conv that are closed under subspaces and contain Top. On the other hand, we study the category PrTop of pretopological spaces that lies in...

Reiner and Webb (preprint, 2002) compute the Sn-module structure for the complex of injective words. This paper refines their formula by providing a Hodge type decomposition. Along the way, this paper proves that the simplicial boundary map interacts in a nice fashion with the Eulerian idempotents. The Laplacian acting on the top chain group in the complex of injective words is also shown to eq...

One of the main tools to classify C∗-algebras is the study of its projections and its unitaries. It was proved by Cuntz in [Cun81] that if A is a purely infinite simple C∗-algebra, then the kernel of the natural map for the unitary group U(A) to the Ktheory groupK1(A) is reduced to the connected component U(A), i.e. A isK1-injective (see §3). We study in this note a finitely generated C∗-algebr...