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Covering, Correspondence and Noncommutative Geometry

 

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  • Product Description
 

We construct an additive category whose objects are embedded graphs (or in particular knots) in the 3-sphere and where morphisms are formal linear combinations of 3-manifolds. Our definition of correspondences relies on the Alexander branched covering theorem, which shows that all compact oriented 3-manifolds can be realized as branched coverings of the 3-sphere, with branched locus an embedded (not necessarily connected) graph. The way in which a given 3-manifold is realized as a branched cover is highly not unique. An interesting homology theory for knots and links that we consider here is the one introduced by Khovanov. We recall the basic definition and properties of Khovanov homology and we give some explicit examples of how it is computed for very simple cases such as the Hopf link. We also recall, the construction of the cobordism group for links and for knots and their relation. We then consider the question of constructing a similar cobordism group for embedded graphs in the 3-sphere.

Product Specifications
SKU :COC93445
AuthorAhmad Zainy Al-Yasry
LanguageEnglish
BindingPaperback
Number of Pages108
Publishing Year2011-08-30T00:00:00.000
ISBN978-3845412627
Edition1 st
Book TypeAlgebra
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00