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On Maps from Loop Suspensions to Loop Spaces and the Shuffle Relations on the Cohen Groups
 
Jie Wu :  National University of Singapore, Singapore, Republic of Singapore
On Maps from Loop Suspensions to Loop Spaces and the Shuffle Relations on the Cohen Groups
eBook ISBN:  978-1-4704-0455-0
Product Code:  MEMO/180/851.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $33.00
Add to cart
On Maps from Loop Suspensions to Loop Spaces and the Shuffle Relations on the Cohen Groups
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On Maps from Loop Suspensions to Loop Spaces and the Shuffle Relations on the Cohen Groups
Jie Wu :  National University of Singapore, Singapore, Republic of Singapore
eBook ISBN:  978-1-4704-0455-0
Product Code:  MEMO/180/851.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $33.00
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 180; 2006; 64 pp
    MSC: Primary 55; Secondary 18; 20

    The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie\((n)\), as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.
  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Maps from loop suspensions to loop spaces
    • 2. Shuffle relations
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 180; 2006; 64 pp
MSC: Primary 55; Secondary 18; 20

The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie\((n)\), as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.
  • Chapters
  • Introduction
  • 1. Maps from loop suspensions to loop spaces
  • 2. Shuffle relations
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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