Two Aspects of Topology in Graph Configuration Spaces

A graph configuration space is generated by the movement of a finite number of robots on a graph. These configuration spaces of points in a graph are topologically interesting objects. By using local, combinatorial properties, we define a new classification of graphs whose configuration spaces are pseudomanifolds with boundary. In algebraic topology, graph configuration spaces are closely related to classical braid groups, which can be described as fundamental groups of configuration spaces of points in the plane. We examine this relationship by finding a presentation for the fundamental group of one graph configuration space.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2005

Author dc:creator

• Ison, Molly Elizabeth

Chair dc:contributor.committeechair

• Haskell, Peter E.

Committee members dc:contributor.committeemember

• Brown, Ezra A.
• Farkas, Daniel R.

• fundamental group
• pseudomanifold with boundary
• manifold
• braid group
• graph
• configuration space

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-10072005-173425

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/29214