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Control and Relaxation over the Circle
 
Bruce Hughes :  Vanderbilt University, Nashville, TN
Stratos Prassidis :  Vanderbilt University, Nashville, TN
Control and Relaxation over the Circle
eBook ISBN:  978-1-4704-0282-2
Product Code:  MEMO/145/691.E
List Price: $51.00
MAA Member Price: $45.90
AMS Member Price: $30.60
Add to cart
Control and Relaxation over the Circle
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Control and Relaxation over the Circle
Bruce Hughes :  Vanderbilt University, Nashville, TN
Stratos Prassidis :  Vanderbilt University, Nashville, TN
eBook ISBN:  978-1-4704-0282-2
Product Code:  MEMO/145/691.E
List Price: $51.00
MAA Member Price: $45.90
AMS Member Price: $30.60
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 145; 2000; 96 pp
    MSC: Primary 19; 57; 55

    We formulate and prove a geometric version of the Fundamental Theorem of Algebraic K-Theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a finite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric version of the Fundamental Theorem of Lower Algebraic K-Theory. The main new innovation is a geometrically defined Nil space.
    Readership

    Graduate students and research mathematicians interested in algebraic topology and algebraic \(K\)-theory.
  • Table of Contents
     
     
    • Chapters
    • 1. Introduction and statement of results
    • 2. Moduli spaces of manifolds and maps
    • 3. Wrapping-up and unwrapping as simplicial maps
    • 4. Relaxation as a simplicial map
    • 5. The Whitehead spaces
    • 6. Torsion and a higher sum theorem
    • 7. Nil as a geometrically defined simplicial set
    • 8. Transfers
    • 9. Completion of the proof
    • 10. Comparison with the lower algebraic nil groups
  • 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: 145; 2000; 96 pp
MSC: Primary 19; 57; 55

We formulate and prove a geometric version of the Fundamental Theorem of Algebraic K-Theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a finite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric version of the Fundamental Theorem of Lower Algebraic K-Theory. The main new innovation is a geometrically defined Nil space.
Readership

Graduate students and research mathematicians interested in algebraic topology and algebraic \(K\)-theory.
  • Chapters
  • 1. Introduction and statement of results
  • 2. Moduli spaces of manifolds and maps
  • 3. Wrapping-up and unwrapping as simplicial maps
  • 4. Relaxation as a simplicial map
  • 5. The Whitehead spaces
  • 6. Torsion and a higher sum theorem
  • 7. Nil as a geometrically defined simplicial set
  • 8. Transfers
  • 9. Completion of the proof
  • 10. Comparison with the lower algebraic nil groups
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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