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Titlebook: Advances in Topological Quantum Field Theory; Proceedings of the N John M. Bryden Conference proceedings 2004 Springer Science+Business Med

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Improper and Nonstandard Models,–strand knots’, closures of the simplest rational tangles. This data allows us to make certain conjectures about the growth rate of the coefficients in Ohtsuki series generally, based on which we introduce an invariant which we call the .(.) of a manifold . (not to be confused with slopes in hyperbo
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Conditionals in Exponential Families,roblems in classical Knot Theory and we develop techniques that allow us to study them: Lagrangian tangles, skein modules and Burnside groups. The method of Burnside groups of links was discovered and developed only half a year after the last talk was delivered in Kananaskis2..Keywords: knot, 3-move
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Conditionals in Exponential Families,n .3 has a non-trivial torsion part. We give a size restriction on the Khovanov homology of almost alternating links. We relate the Khovanov homology of the connected sum of a link diagram with the Hopf link to the Khovanov homology of the diagram via a short exact sequence of homology and prove tha
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Improper and Nonstandard Models,nd Hopf algebra approach to renormalization are exploited. It is proved that the algebra of graphs with Kontsevich graph homology differential and Kreimer’s coproduct is a DG-coalgebra. The weights of the corresponding expansions are proved to be cycles of the DGcoalgebra of Feynman graphs, leading
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