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The Topology of Spaces of Polygons

FROMM, VIKTOR (2011) The Topology of Spaces of Polygons. Doctoral thesis, Durham University.

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We study the topology of spaces of polygons in Euclidean space, viewed up to translations. The main results concern the structure of the homology groups and of the cohomology rings of the spaces. In particular, it is shown that the spaces are classified by their cohomology rings. A principal tool used in the proofs is a new lacunary principle for Morse-Bott functions, which may be of independent interest. Several applications are discussed.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Keywords:Polygon Space, Linkage, Lacunary Principle, Morse-Bott Function, Cohomology
Faculty and Department:Faculty of Science > Mathematical Sciences, Department of
Thesis Date:2011
Copyright:Copyright of this thesis is held by the author
Deposited On:12 Oct 2011 10:54

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