Leon Hardy

A Construction of a Hopf Algebra for Manifolds

A Construction of a Hopf Algebra for Manifolds of 2 and 3 Dimensions with Applcations

• Broschiertes Buch

Produktbeschreibung

We assume the combinatorial viewpoint of Joni and Rota in using Hopf algebras to separate and build an object from its fundamental pieces. We construct the Hopf algebra of polynomials and determine its endomorphisms and automorphisms. Then, the set of orientable, low-dimensional manifolds with and without boundary can be given a Hopf algebraic structure with the connected sum as the multiplication and the disjoint union as the addition. The automorphisms prove useful when we consider the Prime Factorization Theorems of low-dimensional manifolds. Factorization systems of this type often enable one to classify manifolds in a given dimension. When the classification system of low-dimensional manifolds can be given a Hopf algebraic structure, we show that the Hopf algebraic structure yields a categorical equivalence. We briefly discuss generalizing these results to include to higher dimensional manifolds.

Produktdetails

• Verlag: LAP Lambert Academic Publishing
• Seitenzahl: 100
• Erscheinungstermin: 22. Juli 2010
• Englisch
• Abmessung: 220mm x 150mm x 6mm
• Gewicht: 168g
• ISBN-13: 9783838380568
• ISBN-10: 3838380568
• Artikelnr.: 31073970

Autorenporträt

Leon Hardy (University of South Florida St. Petersburg) is a mathematician and physicist. His recent work has focused on stochastic Cohen-Grossberg neural network equations, nonlinear dynamic analysis on human performance with neural network applications, relativistic quantum mechanics fractional derivatives and robotics.