Free rank of symmetry of products of Dold manifolds

Article Type

Research Article

Publication Title

Proceedings of the Edinburgh Mathematical Society

Abstract

Dold 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 ℤ2 cohomologically trivially on a finite CW-complex homotopy equivalent to Πi=1k P(2mi,ni), then G ≅ (ℤ2)l for some l ≤ 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.

First Page

117

Last Page

132

DOI

https://10.1017/S0013091523000068

Publication Date

2-1-2023

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