Low-dimensional topology : proceedings of the Conference on Topology in Low Dimension, Bangor, 1979 / edited by R. Brown and T.L. Thickstun.

Includes bibliographical references.

Print version record.

This volume consists of the proceedings of a conference held at the University College of North Wales (Bangor) in July of 1979. It assembles research papers which reflect diverse currents in low-dimensional topology. The topology of 3-manifolds, hyperbolic geometry and knot theory emerge as major themes. The inclusion of surveys of work in these areas should make the book very useful to students as well as researchers.

Cover; Title; Copyright; Contents; Dedication; Acknowledgements; Preface; Addresses of contributors; Part 1: 3-manifolds; The classification of compact 3-manifolds; REFERENCES; Hyperbolic geometry and 3-manifolds; REFERENCES; Sewing-up link exteriors; Abstract; 1. The construction; 2. Algebra; 3. Homology handles; 4. Homology spheres; 5. Property R; 6. Fibred knots; 7. Cobordisms; 8. Questions; REFERENCES; Periodic transformations in homology 3-spheres and the Rohlin invariant; 1. Introduction; 2. Preliminary Definitions and Constructions.; 3. Proof of the Lemma; REFERENCES

Part 2: Knot theoryThe universal abelian cover of a link; 1. Introduction; 2. The Algorithm; 3. Homology of the cover; 4. Cobordism Invariance of Signature; REFERENCES; Levine's theorem -- a remark; REFERENCES; The factorisation of knots; 0. Introduction; 1. The classical case; 2. Finite Factorisation in Higher Dimensions; 3. Non-unique Factorisation for 3-knots; 4. Some Unique Factorisation; 6. Stop Press; References; Seven excellent knots; 1. The basic setup; 2. The formalism for 2-bridge knots; 3. Three 2-bridge knots; 3(a) The knot 52; 3(b) The knot 77; 4. Conjectures for 2-bridge knots

5. Three bridge knots5(a) The knot 821; 5(b) The knot 943; 5(c) The knot 935; REFERENCES; Part 3: Two-dimensional homotopy theory; Identities among relations; Introduction; 1. Presentations and identities; 2. Pre-crossed and crossed modules; 3. Free Crossed modules; 4. The Associated chain complex; 5. Relation with 2-dimensional CW-complexes; 6. Peiffer transformations; 7. Aspherical 2-complexes and aspherical presentations; 8. The identity property; 9 . Examples and an unsettled problem of J.H.C. Whitehead.; REFERENCES

On Peiffer transformations, link diagrams and a question of J.H.C. WhiteheadIntroduction; 1. A Peiffer trivial identity sequence which does not collapse.; 2. On Peiffer transformations, and link diagrams.; Higher-dimensional group theory; 1. Introduction; 2. The fundamental groupoid; 3. Proof of Theorem 1; 4. Double groupoids; 5. Thin elements; 6. Interpretation; 7. Still higher dimensions; 8. Crossed complexes; REFERENCES; Part 4: 4-manifolds; Actions of compact connected groups on 4-manifolds; 1. Introduction; 2. Equivariant classification.; 3. Topological classification.; REFERENCES

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