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Topic: Deck transformations - who invented 'em?
Replies: 2   Last Post: Mar 23, 2006 3:38 PM

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Roland Franzius

Posts: 422
Registered: 12/7/04
Re: Deck transformations - who invented 'em?
Posted: Mar 23, 2006 3:38 PM
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colin.mclarty@case.edu schrieb:
> 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.
>


It seems to be Hurwitz in Math. Ann. 39 (1891) who as one of the first
used the concept of regular permutations for branches of riemann
surfaces seen as multiple covers of the riemann sphere.

Springer has the table of contents as a pixelpdf online. So somebody has
to go to the library.

--

Roland Franzius




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