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Re: Deck transformations - who invented 'em?
Posted:
Mar 23, 2006 2:58 PM
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Probably the best single answer is Poincare. Vanden Eynde's history of
homotopy introduces the universal cover as a part of Poincare's 1883
work on uniformization, using analytic continuation. ("Development of
the concept of homotopy" in I, M, James HISTORY OF TOPOLOGY, p. 82).
That would involve both aspects that you asked about.
Vanden Eynde (so far as I can see) does not really say Poincare was the
first. Probably it is just too complicated a question when you go into
detail.
The themes go back to Abel and Cauchy on Abelian integrals and analytic
continuation--in hindsight that was all about connecting paths of
integration to series (with radii of convergence) and so to patches
covering a domain. It was not clearly understood in terms of covering
surfaces until Riemann, and then people took decades to get clear on
Riemann surfaces.
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