All Questions

I am interested in a reference with a detailed (as simple and topological as possible) proof of the following fact: Theorem. A principal $\mathrm{SO}(3)$-bundle on a compact oriented 4-manifold are ...

I am trying to understand an argument made by Kobayashi (https://projecteuclid.org/download/pdf_1/euclid.tmj/1178245006, page 35) in his construction of a principal $S^1$-bundle with connection $1$-...

I am aware of classification theorems for principal bundles, vector bundles, and covering spaces $\pi:E\to B$ over a fixed base space $B$. Principal and vector bundles over $B$ are classified by ...

Preamble: Let $X$ be a simply connected smooth manifold and $P \to X$ be a principal $T^\ell$ bundle on it. Let $\phi$ be a smooth action of $T^k$ on $X$. The paper "Lifting compact group actions ...

The Gauss-Bonnet formula gives a topological invariant as an integral over a local density on the given manifold. In particular, when there is a boundary, GB formula has to be supplemented by a ...