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Analytic Structures on Topological Manifolds

  • Neculai S. Teleman
Chapter

Abstract

The aim of this part is to show the reader the classification of analytic structures on topological manifolds. This discussion should show that passing from an analytic structure \(\mathcal {C}\) to a more regular one \(\mathcal {C}^{\prime }\) implies two things: (1) the passage is not ever possible, i.e. there are obstructions, (2) even if the passage is possible, the resulting structures \(\mathcal {C}^{\prime }\)might be not\(\mathcal {C}^{\prime }\)-equivalent. The reader is invited to appreciate Sullivan result (Sullivan and Sullivan, Geometric topology. Localisation. Periodicity and Galois Symmetry. The 1970 MIT Notes. Ed. A. Ranicki) which states that in dimension ≠ 4 the passage from the category of topological manifolds to quasi-conformal/Lipschitz manifolds is always possible, in a unique way.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Neculai S. Teleman
    • 1
  1. 1.Dipartimento di Scienze MatematicheUniversità Politecnica delle MarcheAnconaItaly

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