Floyd's manifold is a conjugation space

TL;DR

This paper proves that the 10-dimensional Floyd manifold admits a cyclic group action making it a conjugation manifold, with its fixed point submanifold's cohomology scaled down by degree.

Contribution

It establishes the existence of a cyclic group action on Floyd's manifold that turns it into a conjugation space, revealing new symmetry properties.

Findings

Floyd's 10-dimensional manifold admits a cyclic group action.

The fixed point submanifold's cohomology is isomorphic to the original, scaled by degree.

The manifold is shown to be a conjugation manifold.

Abstract

We prove that there is an action of the cyclic group $\mathbf{C}_2$ on the $10$-dimensional Floyd manifold which turns it into a conjugation manifold. The submanifold of fixed points is the $5$-dimensional Floyd manifold, whose cohomology is isomorphic to that of the large one, scaled down by dividing the cohomological degree by a factor two.