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Two-Dimensional Homotopy and Combinatorial Group Theory

Two-Dimensional Homotopy and Combinatorial Group Theory

Part of London Mathematical Society Lecture Note Series

C. Hog-Angeloni, W. Metzler, A. J. Sieradski, M. P. Latiolais, M. Dyer, W. Bogley, S. J. pride, G. Huck, S. Rosebrock, M. Lustig, I. Hambleton, M. Kreck, S. Matveev, D. Rolfsen
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  • Date Published: December 1993
  • availability: Available
  • format: Paperback
  • isbn: 9780521447003

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About the Authors
  • Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.

    • Suitable for some graduate courses
    • Contributions have been woven together to form a lucid account of combinatorial theory
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    Product details

    • Date Published: December 1993
    • format: Paperback
    • isbn: 9780521447003
    • length: 428 pages
    • dimensions: 227 x 151 x 21 mm
    • weight: 0.592kg
    • contains: 115 b/w illus.
    • availability: Available
  • Table of Contents

    1. Geometric aspects of two-dimensional complexes C. Hog-Angeloni and W. Metzler
    2. Algebraic topology for two-dimensional complexes A. J. Sieradski
    3. Homotopy and homology classification of 2-complexes M. P. Latiolais
    4. Crossed modules and P2 homotopy modules M. Dyer
    5. Calculating generators of P2 W. Bogley and S. J. pride
    6. Applications of diagrams to decision processes G. Huck and S. Rosebrock
    7. Fox ideals, N-torsion and applications to groups and 3-manifolds M. Lustig
    8. (Singular) 3-manifolds C. Hog-Angeloni and A. Sieradski
    9. Cancellation results for 2-complexes and 4-manifolds and some applications I. Hambleton and M. Kreck
    10. J. H. C. Whitehead's asphericity question W. Bogley
    11. Zeeman's collapsing conjecture S. Matveev and D. Rolfsen
    12. The Andrews-Curtis conjecture and its generalizations C. Hog-Angeloni and W. Metzler.

  • Editors

    Cynthia Hog-Angeloni, Johann Wolfgang Goethe-Universität Frankfurt

    Wolfgang Metzler, Johann Wolfgang Goethe-Universität Frankfurt

    Allan J. Sieradski, University of Oregon

    Contributors

    C. Hog-Angeloni, W. Metzler, A. J. Sieradski, M. P. Latiolais, M. Dyer, W. Bogley, S. J. pride, G. Huck, S. Rosebrock, M. Lustig, I. Hambleton, M. Kreck, S. Matveev, D. Rolfsen

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