 
Summary: The A Deformation Theory of a Point
and the Derived Categories of Local
CalabiYaus
Edward Paul Segal
Imperial College London
Department of Mathematics
Thesis presented for the degree of
Doctor of Philosophy
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Abstract
Let A be an augmented algebra over a semisimple algebra S. We
show that the Ext algebra of S as an Amodule, enriched with its natural
Ainfinity structure, can be used to reconstruct the completion of A at the
augmentation ideal. We use this technical result to justify a calculation
in the physics literature describing algebras that are derived equivalent
to certain noncompact CalabiYau threefolds. Since the calculation pro
duces superpotentials for these algebras we also include some discussion
of superpotential algebras and their invariants.
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Contents
