Skip to content
Register Sign in Wishlist

Ends of Complexes


Part of Cambridge Tracts in Mathematics

  • Date Published: March 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521055192

£ 45.99

Add to cart Add to wishlist

Other available formats:
Hardback, eBook

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour at infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory.

    • Ranicki is a well-known author
    • This book ties up all the loose ends of the subject
    • Features a blend of geometric topology, algebraic topology and algebra, designed to appeal to readers with background in only one of these disciplines
    Read more

    Reviews & endorsements

    'The book gathers together the main strands of the theory of ends of manifolds from the last thirty years and presents a unified and coherent treatment of them. It also contains authoritative expositions of certain topics in topology such as mapping tori and telescopes, often omitted from textbooks. It is thus simultaneously a research monograph and a useful reference.' Proceedings of the Edinburgh Mathematical Society

    'This is a highly specialized monograph which is very clearly written and made as accessible for the reader as possible … It is absolutely indispensable for any specialist in the field.' European Mathematical Society

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: March 2008
    • format: Paperback
    • isbn: 9780521055192
    • length: 380 pages
    • dimensions: 228 x 151 x 21 mm
    • weight: 0.576kg
    • availability: Available
  • Table of Contents

    Chapter summaries
    Part I. Topology at Infinity:
    1. End spaces
    2. Limits
    3. Homology at infinity
    4. Cellular homology
    5. Homology of covers
    6. Projective class and torsion
    7. Forward tameness
    8. Reverse tameness
    9. Homotopy at infinity
    10. Projective class at infinity
    11. Infinite torsion
    12. Forward tameness is a homotopy pushout
    Part II. Topology Over the Real Line:
    13. Infinite cyclic covers
    14. The mapping torus
    15. Geometric ribbons and bands
    16. Approximate fibrations
    17. Geometric wrapping up
    18. Geometric relaxation
    19. Homotopy theoretic twist glueing
    20. Homotopy theoretic wrapping up and relaxation
    Part III. The Algebraic Theory:
    21. Polynomial extensions
    22. Algebraic bands
    23. Algebraic tameness
    24. Relaxation techniques
    25. Algebraic ribbons
    26. Algebraic twist glueing
    27. Wrapping up in algebraic K- and L-theory
    Part IV. Appendices

  • Resources for

    Ends of Complexes

    Bruce Hughes, Andrew Ranicki

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact

  • Authors

    Bruce Hughes, Vanderbilt University, Tennessee

    Andrew Ranicki, University of Edinburgh

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.