Conjugations on 6-manifolds with free integral cohomology

In this article, we show the existence of conjugations on many smooth simply-connected spin 6-manifolds with free integral cohomology. In a certain class the only condition on X ⁶ to admit a conjugation with fixed point set M ³ is the obvious one: the existence of a degree-halving ring isomorphism between the \mathbb Z₂{\mathbb Z_2}-cohomologies of X and M. As a consequence certain 6-manifolds, for which Puppe (J Fixed Point Theory Appl 2(1):85–96, 2007) proved the non-existence of non-trivial orientation-preserving finite group actions, do admit many involutions.