By Friedhelm Waldhausen
Since its creation through Friedhelm Waldhausen within the Nineteen Seventies, the algebraic K-theory of areas has been famous because the major instrument for learning parametrized phenomena within the concept of manifolds. even though, an entire evidence of the equivalence pertaining to the 2 components has now not seemed previously. This ebook offers any such facts, basically finishing Waldhausen's application from greater than thirty years ago.
the most result's a solid parametrized h-cobordism theorem, derived from a homotopy equivalence among an area of PL h-cobordisms on an area X and the classifying area of a class of easy maps of areas having X as deformation retract. the graceful and topological effects then persist with by way of smoothing and triangulation theory.
The evidence has major components. The essence of the 1st half is a "desingularization," enhancing arbitrary finite simplicial units to polyhedra. the second one half compares polyhedra with PL manifolds by way of a thickening strategy. the various concepts and effects built may be worthy in different connections.
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