COSTA, ARMINDO,EMANUEL (2010) Topological Complexity of Configuration Spaces. Doctoral thesis, Durham University.
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In this thesis we study the homotopy invariant TC(X); the topological complexity of a space X. This invariant, introduced by Farber in , was originally motivated by a problem in Robotics; the motion planning problem. We study relations between the topological complexity of a space and its fundamental group, namely when the fundamental group is ”small”, i.e. either has small order or small cohomological dimension. We also apply the navigation functions technique introduced in  to the study of the topological complexity of projective and lens spaces. In particular, we introduce a class of navigation functions on projective and lens spaces. It is known () that the topological complexity of a real projective space equals one plus its immersion dimension. A similar approach to the immersion dimension of some lens spaces has been suggested in . Finally, we study the topological complexity (and other invariants) of random right-angled Artin groups, i.e. the stochastic behaviour of the topological complexity of Eilenberg-MacLane spaces of type K(G, 1), where G is a right-angled Artin group associated to a random graph.
|Item Type:||Thesis (Doctoral)|
|Award:||Doctor of Philosophy|
|Keywords:||topological complexity; navigation functions; random graph groups|
|Faculty and Department:||Faculty of Science > Mathematical Sciences, Department of|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||11 May 2011 16:23|