Abstract
AbstractDold manifolds $P(m,n)$ are certain twisted complex projective space bundles over real projective spaces and serve as generators for the unoriented cobordism algebra of smooth manifolds. The paper investigates the structure of finite groups that act freely on products of Dold manifolds. It is proved that if a finite group G acts freely and $ \mathbb{Z}_2 $ cohomologically trivially on a finite CW-complex homotopy equivalent to ${\prod_{i=1}^{k} P(2m_i,n_i)}$, then $G\cong (\mathbb{Z}_2)^l$ for some $l\leq k$ (see Theorem A for the exact bound). We also determine some bounds in the case when for each i, ni is even and mi is arbitrary. As a consequence, the free rank of symmetry of these manifolds is determined for cohomologically trivial actions.
Publisher
Cambridge University Press (CUP)
Reference33 articles.
1. KU-groups of Dold manifolds;Fujii;Osaka J. Math.,1966
2. (26) Paiva, T. F. V. and dos Santos, E. L. . Cohomology algebra of orbit spaces of free involutions on some Wall manifolds (2021), available at https://arxiv.org/abs/2010.10599.pdf.
3. Determination of the Cobordism Ring
4. THE COHOMOLOGY RING OF ORBIT SPACES OF FREE -ACTIONS ON SOME DOLD MANIFOLDS
5. On the rank of abelian groups acting freely on(S n ) k