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Real Computable Manifolds and Homotopy Groups

  • Wesley Calvert
  • Russell Miller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5715)

Abstract

Using the model of real computability developed by Blum, Cucker, Shub, and Smale, we investigate the difficulty of determining the answers to several basic topological questions about manifolds. We state definitions of real-computable manifold and of real-computable paths in such manifolds, and show that, while BSS machines cannot in general decide such questions as nullhomotopy and simple connectedness for such structures, there are nevertheless real-computable presentations of paths and homotopy equivalence classes under which such computations are possible.

Keywords

Computability Blum-Shub-Smale computability homotopy manifold 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Wesley Calvert
    • 1
  • Russell Miller
    • 2
    • 3
  1. 1.Department of Mathematics and StatisticsMurray State UniversityMurrayU.S.A.
  2. 2.Queens College of CUNYFlushing, NYUSA
  3. 3.The CUNY Graduate CenterNew York, NYUSA

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