Control and Relaxation Over the Circle (Memoirs of the American Mathematical Society)

Control and Relaxation Over the Circle (Memoirs of the American Mathematical Society)

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Description

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.

Contents

Introduction and statement of results Moduli spaces of manifolds and maps Wrapping-up and unwrapping as simplicial maps Relaxation as a simplicial map The Whitehead spaces Torsion and a higher sum theorem Nil as a geometrically defined simplicial set Transfers Completion of the proof Comparison with the lower algebraic nil groups Appendix A. Controlled homotopies on mapping tori Bibliography.

Product Details

  • ISBN13: 9780821820698
  • Format: Paperback
  • Number Of Pages: 96
  • ID: 9780821820698
  • ISBN10: 0821820699

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