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A fibration of ${mathbb R}^n$ by oriented copies of ${mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and Tabachnikov. A classification of smooth fibrations of ${mathbb R}^3$ by skew oriented lines was given by Salvai, in analogue with the classification of oriented great circle fibrations of $S^3$ by Gluck and Warner. We show that Salvais classification has a topological variation which generalizes to characterize all continuous fibrations of ${mathbb R}^n$ by skew oriented copies of ${mathbb R}^p$. We show that the space of fibrations of ${mathbb R}^3$ by skew oriented lines deformation retracts to the subspace of Hopf fibrations, and therefore has the homotopy type of a pair of disjoint copies of $S^2$. We discuss skew fibrations in the complex and quaternionic setting and give a necessary condition for the existence of a fibration of ${mathbb C}^n$ (${mathbb H}^n$) by skew oriented copies of ${mathbb C}^p$ (${mathbb H}^p$).
We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the homotopy typ
We show that in a fibration the coformality of the base space implies the coformality of the total space under reasonable conditions, and these conditions can not be weakened. The result is partially dual to the classical work of Lupton cite{Lup} on
A smooth fibration of $mathbb{R}^3$ by oriented lines is given by a smooth unit vector field $V$ on $mathbb{R}^3$, for which all of the integral curves are oriented lines. Such a fibration is called skew if no two fibers are parallel, and it is calle
Given a path-connected space $X$ and $Hleqpi_1(X,x_0)$, there is essentially only one construction of a map $p_H:(widetilde{X}_H,widetilde{x}_0)rightarrow(X,x_0)$ with connected and locally path-connected domain that can possibly have the following t
We prove that the sectional category of the universal fibration with fibre X, for X any space that satisfies a well-known conjecture of Halperin, equals one after rationalization.