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Control and Relaxation over the Circle, PDF eBook

Control and Relaxation over the Circle PDF

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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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