8 papers
The first homology of square-section braid groups
Minh Pham, Nicholas Wawrykow, Jacob Zweiback
We compute the first homology of the unordered configuration space of open unit-squares in the by rectangle for all positive integers , , and . Letting and…
A discrete model for surface configuration spaces
Nicholas Wawrykow
One of the primary methods of studying the topology of configurations of points in a graph and configurations of disks in a planar region has been to examine discrete combinatorial…
The sequential (distributional) topological complexity of the ordered configuration space of disks in a strip
Nicholas Wawrykow
How hard is it to program robots to move about a long narrow aisle while making a series of intermediate stops, provided only of the robots can fit across the width o…
The topological complexity of the ordered configuration space of disks in a strip
Nicholas Wawrykow
How hard is it to program robots to move about a long narrow aisle such that only of them can fit across the width of the aisle? In this paper, we answer that question by c…
Homology Generators and Relations for the Ordered Configuration Space of a Star Graph
Nicholas Wawrykow
We study the ordered configuration spaces of star graphs. Inspired by the representation stability results of Church--Ellenberg--Farb for the ordered configuration space of a manif…
Representation Stability for Disks in a Strip
Nicholas Wawrykow
We consider the ordered configuration space of open unit-diameter disks in the infinite strip of width . In the spirit of Arnol'd and Cohen, we provide a finite presentation…
On the symmetric group action on rigid disks on a strip
Nicholas Wawrykow
In this paper we decompose the rational homology of the ordered configuration space of open unit-diameter disks on the infinite strip of width as a direct sum of induced $S…
Secondary representation stability and the ordered configuration space of the once-punctured torus
Nicholas Wawrykow
In this paper we study stability patterns in the homology of the ordered configuration space of the once-punctured torus. In the last decade Church and Church-Ellenberg-Farb proved…