Summary:

The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps $U: M\to \text{SU}_{N_F}$ he thinks of the meson fields as of global sections in a bundle $B(M,\text{SU}_{N_F},G)=P(M,G)\times_G \text{SU}_{N_F}$. For calculations within the skyrmion bundle the author introduces by means of the socalled equivariant cohomology an analogue of the topological charge and the WessZumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with $N_F\leq 6$, one has $$ H^{*}(EG\times_G \text{SU}_{N_F})\cong H^{*}(\text{SU}_{N_F})^G \cong \text{S}({\underline G}^{*})\otimes H^{*}(\text{SU}_{N_F}) \cong H^{*}(BG)\otimes H^{*}(\text{SU}_{N_F}), $$ where $EG(BG,G)$ is the universal bundle for the Lie group $G$ and $\underline G$ is the Lie algebra of $G$. (English) 