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RECURSIVELY GENERATING FORMALITY QUASI-ISOMORPHISMS WITH APPLICATIONS TO DEFORMATION QUANTIZATION
Schneider, Geoffrey Ernest
Schneider, Geoffrey Ernest
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Thesis/Dissertation
Date
2017
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Mathematics
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http://dx.doi.org/10.34944/dspace/2308
Abstract
Formality quasi-isomorphisms Cobar(C) -> O are a necessary component of the machinery used in deformation quantization to produce quantized algebras of observables, however they are often constructed via transcendental methods, resulting in computational difficulties and quasi-isomorphisms defined over extensions of Q We will show that these formality quasi-isomorphisms can be "demystified" for a large class of dg-operads, by showing that they can be constructed recursively via an algorithm that builds them from systems of linear equations over Q, given certain assumptions on H(O).
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