Poénaru (1976) theorem

Let $\Gamma$ be a compact Lie group and let $g_{1},\ldots,g_{r}$ generate the module $\vec{\mathcal{P}}(\Gamma)$ (the space of $\Gamma$ -equivariant polynomial mappings) of $\Gamma$ -equivariant polynomials over the ring $\mathcal{P}(\Gamma)$ (the ring of $\Gamma$ -invariant polynomial). Then $g_{1},\ldots,g_{r}$ generate the module $\vec{\mathcal{E}}(\Gamma)$ (the space of $\Gamma$ -equivariant germs at the origin of $C^{\infty}$ mappings) over the ring $\mathcal{E}(\Gamma)$ (the ring of $\Gamma$ -invariant germs). [GSS]

References

GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
PV Poénaru, V.:Singularités $C^{\infty}$ en Présence de Symétrie. Lecture Notes in Mathematics 510, Springer-Verlag, Berlin, 1976.

Title	Poénaru (1976) theorem
Canonical name	Poenaru1976Theorem
Date of creation	2013-03-22 13:40:59
Last modified on	2013-03-22 13:40:59
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	6
Author	mathcam (2727)
Entry type	Theorem
Classification	msc 37G40