Faithful compact quantum group actions on connected compact metrizable spaces

TL;DR

This paper constructs faithful actions of quantum permutation groups on connected compact metrizable spaces, providing a counterexample to a previous conjecture and advancing understanding of quantum symmetries in topology.

Contribution

It introduces the first known faithful quantum permutation group actions on connected spaces, challenging existing conjectures about quantum symmetries.

Findings

Faithful quantum permutation actions exist on connected spaces.

Disproves Goswami's conjecture about quantum symmetries.

Expands the scope of quantum group actions in topology.

Abstract

We construct faithful actions of quantum permutation groups on connected compact metrizable spaces. This disproves a conjecture of Goswami.