Computing the Fundamental Group of an R-computable Manifold
Wesley Calvert, Russell Miller · 2009
Using the model of R-computability developed by Blum, Cucker, Shub, and Smale, we investigate the diculty of determining the answers to several basic topological questions about manifolds. Under natural denitions of R-computable manifold and R-computable path, we show that, while BSS machines cannot in general decide such questions as nullhomotopy and simple connectedness for such structures, there are nevertheless R-computable presentations of paths and homotopy equivalence classes under which such computations are possible. Indeed, we argue that the appropriate model of computation for homotopy questions is the Turing model, not the BSS model for R.