The standard topological approach to indistinguishable particles formulates exchange
statistics by using the fundamental group to analyze the connectedness of the configuration …

We compute the Lusternik-Schnirelmann category (LS-cat) and the higher topological
complexity ($ TC_s $, $ s\geq2 $) of the" no-$ k $-equal" configuration space Conf $ _k …

In the present paper, we study structural aspects of certain quotients of braid groups and
virtual braid groups. In particular, we construct and study linear representations B n→ GL …

The group of planar (or flat) pure braids on n strands, also known as the pure twin group, is
the fundamental group of the configuration space F n, 3 (ℝ) of n labeled points in ℝ no three …

Small Coxeter groups are precisely the ones for which the Tits representation is integral,
which makes the study of their congruence subgroups relevant. The symmetric group S n …

The twin group T n is a right-angled Coxeter group generated by n-1 involutions, and the
pure twin group PT n is the kernel of the natural surjection from T n onto the symmetric group …

It is known that three-body contact interactions in one-dimensional (1D) n (≥ 3)-body
problems of nonidentical particles can be topologically nontrivial: they are all classified by …

Cactus groups J n are currently attracting considerable interest from diverse mathematical
communities. This work explores their relations to right-angled Coxeter groups and, in …

Abstract Let n≥ 2. Let VB n (resp. VP n) be the virtual braid group (resp. the pure virtual
braid group), and let VT n (resp. PVT n) be the virtual twin group (resp. the pure virtual twin …

Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core
two-body constraints make the configuration space of particles not simply-connected. The …