Analytic Structures on Topological Manifolds

Neculai S. Teleman
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Neculai S. Teleman: Università Politecnica delle Marche, Dipartimento di Scienze Matematiche

Chapter Chapter 4 in From Differential Geometry to Non-commutative Geometry and Topology, 2019, pp 235-241 from Springer

Abstract: 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 C $$\mathcal {C}$$ to a more regular one C ′ $$\mathcal {C}^{\prime }$$ 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 C ′ $$\mathcal {C}^{\prime }$$ might be not C ′ $$\mathcal {C}^{\prime }$$ -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.

Date: 2019
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DOI: 10.1007/978-3-030-28433-6_4

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