$Z^k_2$-actions fixing $\{point\}\cup V^n$

Pedro L. Q. Pergher¹

¹ Departamento de Matemática Universidade Federal de São Carlos Caixa Postal 676 CEP 13.565-905 São Carlos, SP, Brazil

Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 83-97

Résumé

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.

Détail

DOI : 10.4064/fm172-1-6

Keywords: describe equivariant cobordism classification smooth actions mit phi group closed smooth m dimensional manifolds which fixed point set action union cup where point connected manifold dimension description given terms set equivariant cobordism classes involutions fixing cup generalizes lot previously obtained particular cases above question additionally result yields applications namely arbitrary product spheres n dimensional closed manifold odd