The A∞ Deformation Theory of a Point and the Derived Categories of Local Calabi-Yaus

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Title: The A∞ Deformation Theory of a Point and the Derived Categories of Local Calabi-Yaus
Author(s): Segal, Edward Paul
Item Type: Thesis or dissertation
Abstract: Let A be an augmented algebra over a semi-simple algebra S. We show that the Ext algebra of S as an A-module, enriched with its natural A-infinity 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 non-compact Calabi-Yau three-folds. Since the calculation produces superpotentials for these algebras we also include some discussion of superpotential algebras and their invariants.
Publication Date: 2008
Date Awarded: Jul-2008
URI: http://hdl.handle.net/10044/1/1371
Advisor: Thomas, Richard
Author: Segal, Edward Paul
Department: Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Mathematics PhD theses



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