Large orbits, projective Fraisse limits, and the pseudo-arc

TL;DR

This paper demonstrates that the automorphism group of the projective Fraïssé limit, which relates to the pseudo-arc, acts with a comeager orbit on the set of involutions, revealing a rich symmetry structure.

Contribution

It establishes the existence of a comeager conjugacy class of involutions in the automorphism group of the pseudo-arc's Fraïssé limit, linking topological dynamics and continuum theory.

Findings

The automorphism group acts with a comeager orbit on involutions.

The pseudo-arc arises as a natural quotient of the projective Fraïssé limit.

The work connects topological dynamics with the structure of the pseudo-arc.

Abstract

We show that the conjugacy action of the automorphism group ${\rm Aut}(\mathbb{P})$, of the projective Fra\"{i}ss\'{e} limit $\mathbb{P}$, whose natural quotient is the pseudo-arc, on the set of involutions of $\mathbb{P}$, has a comeager orbit.