The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruction and change of orientations by their groups alone. This book arose out of two earlier books "2-Knots and their Groups" and "The Algebraic Characterization of Geometric 4-Manifolds", published by Cambridge University Press for the Australian Mathematical Society and for the London Mathematical Society, respectively. About a quarter of the present text has been taken from these books, and I thank Cambridge University Press for their permission to use this material. The book has been revised in March 2007. For details see the end of the preface.

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Links and Seifert fiber spaces

Four-manifolds, geometries and knots

Hegaard genus of closed orientable Seifert 3-manifolds.

On associe a un enlacement L dans S 3 un groupe O(L), appele le groupe de Π-variete d'orbite de L. On etudie certaines proprietes du groupe O(L) reliees a la geometrie de l'enlacement L

Links and Seifert fiber spaces

Citations

Four-manifolds, geometries and knots

Hegaard genus of closed orientable Seifert 3-manifolds.

The π-orbifold group of a link

Symmetries of nonelliptic Montesinos links

Scindements de Heegaard et groupe des homéotopies des petites variétés de Seifert

Related Papers (5)

Knots and Links

Homotopy Equivalences of 3-Manifolds with Boundaries

Three dimensional manifolds, Kleinian groups and hyperbolic geometry

On irreducible 3-manifolds which are sufficiently large

Dehn surgery on knots