Spaces of homotopy self-equivalences : a survey / John W. Rutter

The present work is a brilliant survey of the results in the area of self-equivalences (homotopy) of a space. Beginning with the 19th century (equivalences of a Riemann surface) right up to the mid 1990’s the author analyzes the main trends which include: (1) based and free homotopy equivalences of surfaces and manifolds, (2) cellular and Postnikov methods; finite-generation and finite presentation, (3) non-simply connected spaces, Whitehead torsion, and (4) the homotopy structure of the space of self-equivalences. More technical questions such as n-type and the algebra of arithmetic groups are placed in the appendices.

While it is clearly impossible to supply proofs for the work of 331 books and papers by dozens of authors, the author manages to convey the ideas behind some of the proofs in a remarkably clear and concise way. The result is a state-of-the-art description of an amazing subject through the middle of the present decade. It will be of great value to anyone who wishes to enter any part of this surprising field. ... (Zentralblatt)