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Higher-Dimensional Knots According to Michel Kervaire
EMS Series of Lectures in Mathematics

Françoise Michel (Université Paul Sabatier, Toulouse, France)
Claude Weber (Université de Genève, Switzerland)

Higher-Dimensional Knots According to Michel Kervaire

ISBN print 978-3-03719-180-4, ISBN online 978-3-03719-680-9
DOI 10.4171/180
July 2017, 144 pages, softcover, 17 x 24 cm.
32.00 Euro

Michel Kervaire wrote six papers which can be considered fundamental to the development of higher-dimensional knot theory. They are not only of historical interest but naturally introduce to some of the essential techniques in this fascinating theory.

This book is written to provide graduate students with the basic concepts necessary to read texts in higher-dimensional knot theory and its relations with singularities. The first chapters are devoted to a presentation of Pontrjagin’s construction, surgery and the work of Kervaire and Milnor on homotopy spheres. We pursue with Kervaire’s fundamental work on the group of a knot, knot modules and knot cobordism. We add developments due to Levine. Tools (like open books, handlebodies, plumbings, …) often used but hard to find in original articles are presented in appendices. We conclude with a description of the Kervaire invariant and the consequences of the Hill–Hopkins–Ravenel results in knot theory.

Keywords: Knots in high dimensions, homotopy spheres, complex singularities