Homotopy monomorphisms and H-splitting in loop space fibrations

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

Splitting Manifold Approximate Fibrations

Suppose M is a topological m-manifold, X is a generalized nmanifold satisfying the disjoint disks property (DDP ), m > n ≥ 5, f : M → X is an approximate fibration, with fiber the shape of a closed topological manifold F , and Y is a closed, 1-LCC, codimension three subset of X. We examine conditions under which f is controlled homeomorphic to an approximate fibration g : M → X such that g|g−1(...

Fibrations and Homotopy Colimits of Simplicial Sheaves

We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the no...

Loop Spaces and Homotopy Operations

We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking value in π∗X. These depend on first algebraically “delooping” the Π-algebra π∗X, using the H-space structure on X, and then trying to realize the delooped Π-algebra.

Two-loop Splitting Amplitudes

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. T...