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We consider the existence of bibundles, in other words locally trivial principal $G$ spaces with commuting left and right $G$ actions. We show that their existence is closely related to the structure of the group $Out(G)$ of outer automorphisms of $G$. We also develop a classifying theory for bibundles. The theory is developed in full generality for $(H, G)$ bibundles for a crossed-module $(H, G)$ and we show with examples the close links with loop group bundles.
We show that on every compact Riemannian 2-orbifold there exist infinitely many closed geodesics of positive length.
In this article, we show the existence of a nontrivial Riemann surface lamination embedded in $mathbb{CP}^2$ by using Donaldsons construction of asymptotically holomorphic submanifolds. Further, the lamination we obtain has the property that each lea
In this paper we prove the existence of Type II singularities for the Ricci flow on $S^{n+1}$ for all $ngeq 2$.
We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold $M$ with only one end if $M$ has asymptotically non-negative sectional curva
Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary $partial M$, admitting a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly la