A structure theorem for bad 3-orbifolds

The Splitting Theorem for Orbifolds

An Algebraic Index Theorem for Orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann–Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the K...

A Quillen Model Structure for Orbifolds

A Quillen model structure on the category of orbifold groupoids is constructed. The fibrant objects for this category are the stacks groupoids and the homotopy category is the category of orbifolds.

Detailed Structure for Freiman ’ s 3 k − 3 Theorem

Let A be a set of k integers. We study Freiman’s inverse problem with small doublings and continue the work of G. A. Freiman, I. Bardaji and D. J. Grynkiewicz by characterizing the detailed structure of A in Theorem 2.2 below when the sumset A + A contains exactly 3k−3 integers. Besides some familiar structures, such a set A can have a configuration composed of “additively minimal triangles.”

Complexity of 3-orbifolds

We extend Matveev’s theory of complexity for 3-manifolds, based on simple spines, to (closed, orientable, locally orientable) 3-orbifolds. We prove naturality and finiteness for irreducible 3-orbifolds, and, with certain restrictions and subtleties, additivity under orbifold connected sum. We also develop the theory of handle decompositions for 3orbifolds and the corresponding theory of normal ...