Higher-dimensional Knots According to Michel Kervaire

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 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. The authors explore Kervaire's fundamental work on the group of a knot, knot modules, and knot cobordism and then consider developments due to Levine. Tools such as open books, handlebodies, and plumbings, which are often used but hard to find in original articles, are presented in appendices. The authors conclude with a description of the Kervaire invariant and the consequences of the Hill Hopkins Ravenel results in knot theory. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.