We show that non-abelian quantum statistics can be studied using certain topological
invariants which are the homology groups of configuration spaces. In particular, we …

We study the problem of computing the homology of the configuration spaces of a finite cell
complex X. We proceed by viewing X, together with its subdivisions, as a subdivisional …

We study geometric presentations of braid groups for particles that are constrained to move
on a graph, ie a network consisting of nodes and edges. Our proposed set of generators …

We show that the homology of ordered configuration spaces of finite trees with loops is
torsion-free. We introduce configuration spaces with sinks, which allow for taking quotients …

We introduce a novel type of stabilization map on the configuration spaces of a graph which
increases the number of particles occupying an edge. There is an induced action on …

For a tree G, we study the changing behaviors in the homology groups H i (B n G) as n
varies, where B n G:= π 1 (UConf n (G)). We prove that the ranks of these homologies can be …

We introduce and study an algorithm that constructs a discrete gradient field on any
simplicial complex. With a computational complexity similar to that of existing methods, our …

We study the category whose objects are trees (with or without roots) and whose morphisms
are contractions. We show that the corresponding contravariant module categories are …

We demonstrate that anyons on wire networks have fundamentally different braiding
properties than anyons in two dimensions (2D). Our analysis reveals an unexpectedly wide …

Let $ K $ be a $ k $-dimensional simplicial complex having $ n $ faces of dimension $ k $,
and $ M $ a closed $(k-1) $-connected PL $2 k $-dimensional manifold. We prove that for …