Celebratio Mathematica — Gordon — Working with Cameron

Working with Cameron: from exceptional surgeries to the L-space conjecture

Works connected to Jean-Claude Hausmann

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C. M. Gordon: “Some aspects of classical knot theory,” pp. 1–60 in Knot theory (Plans-sur-Bex, Switzerland, 1977). Edited by J. C. Hausmann. Lecture Notes in Mathematics 685. Springer (Berlin), 1978. This volume is dedicated to the memory of Christos Demetriou Papakyriakopoulos, 1914–1976. MR 521730 Zbl 0386.57002 incollection

Man’s fascination with knots has a long history, but they do not appear to have been considered from the mathematical point of view until the 19th century. Even then, the unavailability of appropriate methods meant that initial progress was, in a sense, slow, and at the beginning of the present century rigorous proofs had still not appeared. The arrival of algebraic-topological methods soon changed this, however, and the subject is now a highly-developed one, drawing on both algebra and geometry, and providing an opportunity for interplay between them.

The aim of the present article is to survey some topics in this theory of knotted circles in the 3-sphere. Completeness has not been attempted, nor is it necessarily the case that the topics chosen for discussion and the results mentioned are those that the author considers the most important: non-mathematical factors also contributed to the form of the article.

Christos Dimitriou Papakyriakopoulos	Related
Jean-Claude Hausmann	Related