Control and Relaxation over the Circle, by Bruce Hughes and Stratos Prassidis

We formulate and proove 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.


Bruce Hughes <hughes@math.vanderbilt.edu>
Stratos Prassidis <prassie@math.vanderbilt.edu>