Bruce Hughes

Stratos Prassidis

This work formulates and proves 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.

Control and Relaxation over the Circle

Andrew Ranicki

A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.

Bruce Hughes

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