eBook ISBN:  9781470402822 
Product Code:  MEMO/145/691.E 
List Price:  $51.00 
MAA Member Price:  $45.90 
AMS Member Price:  $30.60 
eBook ISBN:  9781470402822 
Product Code:  MEMO/145/691.E 
List Price:  $51.00 
MAA Member Price:  $45.90 
AMS Member Price:  $30.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 145; 2000; 96 ppMSC: Primary 19; 57; 55
We formulate and prove a geometric version of the Fundamental Theorem of Algebraic KTheory which relates the Ktheory of the Laurent polynomial extension of a ring to the Ktheory 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 KTheory. The main new innovation is a geometrically defined Nil space.
ReadershipGraduate 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. Wrappingup 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


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We formulate and prove a geometric version of the Fundamental Theorem of Algebraic KTheory which relates the Ktheory of the Laurent polynomial extension of a ring to the Ktheory 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 KTheory. The main new innovation is a geometrically defined Nil space.
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. Wrappingup 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