# zbMATH — the first resource for mathematics

Cohomology and connection on $$S^1$$-bundles. (English) Zbl 0909.58001
Slovák, Jan (ed.), Proceedings of the 15th Winter School on geometry and physics, Srní, Czech Republic, January 14–21, 1995. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43, 123-132 (1996).
The author applies results on cohomology and connections on $$S^1$$-bundles to the skyrmion bundle in theoretical nuclear physics and generalizes the ungauged Skyrme model in order to treat interactions not only between baryons and mesons but also with electromagnetic fields described by a Maxwell connection on the associated principal bundle.
The article has five paragraphs. First an introduction, then a paragraph on connections on principal $$S^1$$-bundles. The third paragraph is on spectral sequences. For any connection $$\Gamma$$ on the associated principal bundle $$P(M,G)$$ for any given fiber bundle $$B(M,F,G)$$, in the fourth paragraph is treated the problem of $$\Gamma$$-adaptation of the differential forms for $$S^1$$-bundle. Finally, the author applies the results and gauges the Skyrme model for the purpose of treating interactions.
For the entire collection see [Zbl 0884.00042].
##### MSC:
 58A12 de Rham theory in global analysis 55R20 Spectral sequences and homology of fiber spaces in algebraic topology 53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)