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.
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Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
ISBN-13
978-0-8218-2069-8 (9780821820698)
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Schweitzer Klassifikation
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.
