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The first main objective of this proposal is to determine topological and Floer-theoretic obstructions to the existence of embedded Maslov-zero Lagrangian desingularizations of special Lagrangian (SL) cones. In particular, several such obstructions are expected to arise from the application of Contact homology techniques to the boundary of a neighbourhood of the singular point.The second main obje ...
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 FINISHED 

Construction of new G2 manifolds using Calabi-Yau 3-folds (G2 MANIFOLDS)

Start date: Aug 20, 2007, End date: Nov 19, 2008,

...of the existence of a parallel G2-structure on the resulting smooth 7-manifold will involve techniques of non-linear analysis similar to those developed by the proposed scientist in charge, Professor Dominic Joyce when he constructed the first examples of smooth compact G2 manifolds in 1993-4. Such constructions are important both for differential geometry and for super-string and super-gravity th ...
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