Control and Relaxation Over the Circle

Buch | Softcover

96 Seiten

2000
American Mathematical Society (Verlag)
978-0-8218-2069-8 (ISBN)

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Intends to 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. Using methods of controlled topology, this title obtains a geometric version of the Fundamental Theorem of Lower Algebraic K-Theory.

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.

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.

Erscheint lt. Verlag	1.6.2000
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-2069-9 / 0821820699
ISBN-13	978-0-8218-2069-8 / 9780821820698
Zustand	Neuware