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Title: Boundary singularities of functions in symplectic and volume-preserving geometry
Author: Kourliouros, Konstantinos
ISNI:       0000 0004 7233 1095
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2016
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In this thesis we study the classi cation problem of boundary singularities of functions in symplectic and volume-preserving geometry. In particular we generalise several well known theorems concerning the classi cation of isolated singularities of functions and volume forms in the presence of a \boundary", i.e. a germ of a xed smooth hypersurface. The results depend in turn on a generalisation of the relative de Rham cohomology and the corresponding Gauss-Manin theory to the case of isolated boundary singularities and in particular, on a relative version of the so called Brieskorn-Deligne-Sebastiani theorem, concerning the niteness and freeness of certain cohomology modules.
Supervisor: Lamb, Jeroen ; Turaev, Dimitry Sponsor: Imperial College London
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral