# bundles

1. ### A Penrose paragraph on Bundle Cross-section?

I am reading "Road to Reality" by Rogen Penrose. In chapter 15, Fibre and Gauge Connection ,while going through Clifford Bundle, he says: ."""" ........Of course, this in itself does not tell us why the Clifford bundle has no continuous cross-sections. To understand this it will be helpful to...
2. ### A Is the Berry connection compatible with the metric?

Hello, Is the Berry connection compatible with the metric(covariant derivative of metric vanishes) in the same way that the Levi-Civita connection is compatible with the metric(as in Riemannanian Geometry and General Relativity)? Also, does it have torsion? It must either have torsion or not be...
3. ### Restricting Base of Bundle. Which Properties are Preserved?

Hi All, Please let me set things up before the actual question: I have a Lefschetz fibration $f: W^4 \rightarrow S^2$ , where $W^4$ is a closed, oriented manifold, and $S^2$ is the 2-disk. This f is a smooth map with finitely-many singularities {$x_1, x_2,..,x_n$}, so that we have...