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Organizers |
The History of Knot Theory
by
Kenneth A. Perko, Jr.
325 Old Army Road, Scarsdale, New York 10583
Riemann's unreal surfaces begat covering spaces, which Heegaard illustrated in 1898 for functions of two complex variables. Wirtinger chopped them up into bite-sized pieces in 1905, exposing the structure of a knot's complement [cf. Epple, Branch points of algebraic functions and the beginnings of modern knot theory, Historia Mathematica 22 (1995), 384] and that, Gordon and Luecke proved in 1989, explains everything (unlike all those proliferating polynomials). Examples of historically important non-cyclic covering spaces will be exhibited, along with new, improved diagrams of an eponymous pair of knots.
Date received: December 14, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-55.