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Abstract

We describe the equivariant cobordism classification of smooth actions $(M^m,{\mit\Phi })$ of the group $G=Z_2^k$ on closed smooth $m$-dimensional manifolds $M^m$ for which the fixed point set of the action is the union $F=p \cup V^n$, where $p$ is a point and $V^n$ is a connected manifold of dimension $n$ with $n>0$. The description is given in terms of the set of equivariant cobordism classes of involutions fixing $p \cup V^n$. This generalizes a lot of previously obtained particular cases of the above question; additionally, the result yields some new applications, namely with $V^n$ an arbitrary product of spheres and with $V^n$ any $n$-dimensional closed manifold with $n$ odd.