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A simple model for the exotic waves with $I^G(J^{PC})=1^-(1^{-+})$ in thereactions $VP\to VP$, $VP\to PP$, and $PP\to PP$ is constructed beyond thescope of the quark-gluon approach. The model satisfies unitarity andanalyticity and uses as a "priming" the "anomalous" nondiagonal $VPPP$interaction which couples together the four channels $\rho\pi$, $\eta\pi$,$\eta'\pi$, and $K^*\bar K+\bar K^*K$. The possibility of the resonancelikebehavior of the $I^G(J^{PC})=1^-(1^{-+})$ amplitudes belonging to the $\{10\}-\{\bar{10}\}$ and $\{8\}$ representations of SU(3) as well as their mixing isdemonstrated explicitly in the $1.3-1.6$ GeV mass range which, according to thecurrent experimental evidence, is really rich in exotics.Comment: LaTex, 17 pages including 4 figures, version published in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Effective Lagrangian induced by the anomalous Wess-Zumino action and the exotic resonance state withIG(JPC)=