# Article

 Title: Equivariant cohomology of the skyrmion bundle (English) Author: Gross, Christian Language: English Journal: Proceedings of the 16th Winter School "Geometry and Physics" Volume: Issue: 1996 Year: Pages: [87]-96 . Category: math . 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 so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino 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) MSC: 53C80 MSC: 53Z05 MSC: 55N91 MSC: 55R91 MSC: 58A12 MSC: 81V05 idZBL: Zbl 0905.53052 idMR: MR1469024 . Date available: 2009-07-13T21:37:53Z Last updated: 2012-09-18 Stable URL: http://hdl.handle.net/10338.dmlcz/701598 .

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