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Durham e-Theses
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Topological Complexity of Configuration Spaces

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 [15], 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 [20] 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 ([25]) 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 [31]. 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
Thesis Date:2010
Copyright:Copyright of this thesis is held by the author
Deposited On:11 May 2011 16:23

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