Skip to content
Register Sign in Wishlist

Formal Geometry and Bordism Operations


Part of Cambridge Studies in Advanced Mathematics

Matthew Ando, Nathaniel Stapleton, Michael Hopkins
View all contributors
  • Date Published: December 2018
  • availability: In stock
  • format: Hardback
  • isbn: 9781108428033

£ 67.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • This text organizes a range of results in chromatic homotopy theory, running a single thread through theorems in bordism and a detailed understanding of the moduli of formal groups. It emphasizes the naturally occurring algebro-geometric models that presage the topological results, taking the reader through a pedagogical development of the field. In addition to forming the backbone of the stable homotopy category, these ideas have found application in other fields: the daughter subject 'elliptic cohomology' abuts mathematical physics, manifold geometry, topological analysis, and the representation theory of loop groups. The common language employed when discussing these subjects showcases their unity and guides the reader breezily from one domain to the next, ultimately culminating in the construction of Witten's genus for String manifolds. This text is an expansion of a set of lecture notes for a topics course delivered at Harvard University during the spring term of 2016.

    • Gives graduate students the necessary information to conduct their own research without having to search through the literature
    • Covers a broad range of material, presented in a way that makes cross-referencing easy for readers
    • Prepares readers for cross-disciplinary work by bringing together many different fields of mathematics
    Read more

    Reviews & endorsements

    'It has a down-to-earth and inviting style (no small achievement in a book about functorial algebraic geometry). It is elegant, precise, and incisive, and it is strong on both theory and calculation.' Michael Berg, MAA Reviews

    'This book is likely to be quite useful to graduate students in algebraic topology. For years it has been an informal tradition for students of algebraic topology to teach themselves enough of the foundations of algebraic geometry to be able to translate between theorems about Hopf algebroids and theorems about algebraic stacks, and then to proceed to translate, as much as possible, calculations and theorems in algebraic topology into equivalent formulations in terms of moduli stacks of formal groups and related objects. This book does a great service to such students (and their advisors!), as it gives good answers to many of the questions such students inevitably ask.' Andrew Salch, MatSciNet

    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: December 2018
    • format: Hardback
    • isbn: 9781108428033
    • length: 418 pages
    • dimensions: 234 x 157 x 23 mm
    • weight: 0.79kg
    • contains: 15 b/w illus. 4 colour illus.
    • availability: In stock
  • Table of Contents

    Foreword Matthew Ando
    1. Unoriented bordism
    2. Complex bordism
    3. Finite spectra
    4. Unstable cooperations
    5. The σ-orientation
    Appendix A. Power operations
    Appendix B. Loose ends

  • Author

    Eric Peterson, Harvard University, Massachusetts
    Eric Peterson works in quantum compilation for near-term supremacy hardware at Rigetti Computing in Berkeley, California. He was previously a Benjamin Peirce Fellow at Harvard University.


    Matthew Ando, Nathaniel Stapleton, Michael Hopkins

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.