The Geometric Hopf Invariant and Surgery Theory

"The Geometric Hopf Invariant and Surgery Theory" is a comprehensive monograph authored by leading experts in the field. It provides a homotopical foundation for surgery theory on higher-dimensional manifolds. The authors present classical ideas within a modern framework and illustrate how their results extend and generalize existing findings in the literature. A central result of the book is the representation of algebraic surgery theory in relation to the geometric Hopf invariant, a construction in stable homotopy theory that captures double points of embeddings. The book includes numerous illustrative examples and applications of the abstract results, making it of great interest to topologists. It serves as a valuable reference for graduates and researchers who wish to understand how algebraic and geometric topology fit together in the surgery theory of manifolds. This work offers a comprehensive historical approach to the Hopf invariant, double points, and surgery theory, featuring many old and new results.