FROMM, VIKTOR (2011) The Topology of Spaces of Polygons. Doctoral thesis, Durham University.
|PDF - Accepted Version|
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|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||12 Oct 2011 10:54|