The homotopy type of a closed simply connected 4-manifold is determined by the intersection form. The homotopy classes of maps between two such manifolds, however, do not coincide with the algebraic morphisms between intersection forms. Therefore the problem arises of computing the homotopy classes of maps algebraically and determining the law of composition for such maps. This problem is solved in the book by introducing new algebraic models of a 4-manifold. The book has been written to appeal to both established researchers in the field and graduate students interested in topology and algebra. There are many references to the literature for those interested in further reading.

'… this book is heartily recommended to anyone interested in studying homotopy theories from a categorial point of view.'

Source: Zentralblatt MATH

'The reader will obtain very deep information on the structure of relevant categories. The text is very clearly written but the author substantially uses many previous results of his own as well as many other results … the results are so excellent that they deserve some patience and effort.'

Source: EMS Newsletter

'This research monograph covers more than is promised in the title.'

Source: Nieuw Archief voor Wiskunde