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Cover A Construction of a Hopf Algebra for Manifolds by 	Leon Hardy

Download A Construction of a Hopf Algebra for Manifolds by Leon Hardy

  • Authors: Leon Hardy
  • ISBN-13: 3838380568
  • ISBN: 9783838380568
  • Pub. Date: July 2010
  • Publisher: LAP Lambert Academic Publishing
  • Add:Admin
  • Add time:20:24
  • Available formats:PDF, FB2, DJBU, TXT, EPUB, Mobi
  • File status:online

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Discription A Construction of a Hopf Algebra for Manifolds by Leon Hardy:

 OverviewWe 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.This item is Non-Returnable." "Yes, I should think so"; and Laurie thought A Construction of a Hopf Algebra for Manifolds of his own idle days.

"Mother likes to have us out of doors as much A Construction of a Hopf Algebra for Manifolds possible; so we bring our work here, and have nice times. For the fun of it we bring our things in these bags, wear the old hats, use poles to climb the hill, and play pilgrims, as we used to do years ago. We call this hill the 'Delectable Mountain,' for we can look far away and see the country where we hope to live some time.

" Jo pointed, and Laurie Albebra up to examine; for through an opening in the wood one could look across the wide, blue river, the meadows on the other side, far over the outskirts of the great city, to the green hills that rose to meet the sky. The sun was low, and the heavens glowed with the splendor of an autumn sunset. Gold and purple clouds lay on the hill-tops; and rising high into the ruddy light were silvery white peaks, that shone like the airy spires of some Celestial Constructon.

"How beautiful that is!" said Laurie softly, for he was quick to see and feel beauty of any kind. "It's Manifoldx so; and we like to watch it, for it is never the same, but always splendid," replied Amy, wishing she could Maniifolds it.

"Jo talks about the country where we hope to live some time- the real country, she fr, with pigs and chickens and haymaking. It would be nice, but I wish the beautiful country up there was real, and we could ever go to it," said Beth musingly. "There is a lovelier country even Mannifolds that, where we shall go, by and by, when we Manfolds good enough," answered Meg, with her sweet voice. "It seems so long to wait, so hard to do; I want to fly away at once, as those swallows fly, and go in at that splendid gate.

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