$SO(n)$, $SU(n)$, $Sp(n)$-homology Spheres with Codimension Two Principal Orbits
Aiko Nakanishi · Tokyo Journal of Mathematics · 1984
tively.A smooth action of $SO(n),$ $SU(n)$ or $Sp(n)$ on $M$ is called regular if its linear model is given by a representation $k\rho_{n}\oplus trivia1$ representation, $k(\mu_{n})_{R}\oplus trivia1$ representation or $k( u_{n})_{R}\oplus trivia1$ representation, respectively, where $ k\phi$ is the direct sum of $k$ copies of a representation $\phi$ .We shall also say that these representations are regular.In [5], M. Davis and W. C. Hsiang classffied regular* $U(n)$ and $Sp(n)$ -actions on homotopy spheres up to concordance.And in [7], these authors and J. W. Morgan classified regular* $O(n)$ -actions on homotopy spheres up to concordance.In this paper, we treat smooth actions of compact, connected, simple classical Lie groups on homology spheres with linear models, and we shall prove that these actions are completely classified up to equivariant diffeo- morphisms, if they have codimension two principal orbits.When a smooth