In case of Riemannian geometry the connection $\Gamma^i_{jk}$ as is derived from the derivatives of the metric tensor $g_{ij}$ is ought to be symmetric wrt to its lower two indices. But in the case of Non-Riemannian Geometry that need not be the case, so the question is how do you actually construct such connections? Do […]

Let $P$ be a principal $G$-bundle over $B$, and let $G$ act on some space $F$ (feel free to work in your favorite category of spaces, if this helps). Then $\text{Aut}{P}$ (aka the group of gauge transformations of $P$) acts on the space of sections of the associated bundle $P\times_G F$ as follows: if $\alpha\in\text{Aut}P$ […]

I am looking for a textbook that might serve as an introduction to principal bundles, curvature forms and characteristic classes, and perhaps towards 4-manifolds and gauge theory. Currently, the only books I know of in this regard are: “From Calculus to Cohomology” (Madsen, Tornehave) “Geometry of Differential Forms” (Morita) “Differential Forms in Algebraic Topology” (Bott, […]

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