String topology & compactified moduli spaces
Item
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Title
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String topology & compactified moduli spaces
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Identifier
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d_2009_2013:2b95c046109e:10651
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identifier
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10810
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Creator
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Poirier, Katherine,
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Contributor
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Dennis Sullivan
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Date
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2010
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics | Theoretical mathematics | Algebraic Topology | Moduli Spaces | Riemann Surfaces | String Topology | Topology of Manifolds
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Abstract
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The motivation behind this work is to solve the master equation ∂ X = X * X in ⊕ k,ℓHom( P⊗k*,P⊗ ℓ* ) where P* is a chain complex computing HS1* (LM, M), the S 1-equivariant homology of the free loop space LM of a manifold M, relative to constant loops. Here, we solve a modification of this equation: 6X=X*X+A and suggest an avenue for modifying the solution of the second equation to obtain a solution of the master equation. The solution of the second equation is constructed by building a pseudomanifold of string diagrams which has prescribed boundary. The string topology construction describes the action of cellular chains of the pseudomanifold on P *. Further, the pseudomanifold is homeomorphic to a compactification of the moduli space of Riemann surfaces. A second smaller compactification is defined over which string topology operations conjecturally extend.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Mathematics
