Everand Logo

Welcome to Everand!

  • Discover millions of ebooks, audiobooks, and so much more with a free trial

    From $11.99/month after trial. Cancel anytime.

    Characteristic Classes. (AM-76), Volume 76
    Characteristic Classes. (AM-76), Volume 76
    Characteristic Classes. (AM-76), Volume 76
    Ebook338 pages5 hours

    Characteristic Classes. (AM-76), Volume 76

    By John Milnor and James D. Stasheff

    4.5/5

    ()

    Read preview

    About this ebook

    The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.



    In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.



    Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

    LanguageEnglish
    PublisherPrinceton University Press
    Release dateMar 2, 2016
    ISBN9781400881826
    Characteristic Classes. (AM-76), Volume 76
    Author

    John Milnor

    John Milnor is Professor of Mathematics and Co-Director of the Institute for Mathematical Sciences at SUNY, Stony Brook. He is the author of Topology from the Differential Viewpoint, Singular Points of Complex Hypersurfaces, Morse Theory, Introduction to Algebraic K-Theory, Characteristic Classes (with James Stasheff), and Lectures on the H-Cobordism Theorem (Princeton).

    Related to Characteristic Classes. (AM-76), Volume 76

    Titles in the series (100)

    View More
    View More

    Related ebooks

    Mathematics For You

    View More
    View More

    Related podcast episodes

    Related articles

    • UNLIMITED

      How to Build a Search Engine for Mathematics: The Surprising Power of Neil Sloane’s Encyclopedia of Integer Sequences.: The surprising power of Neil Sloane’s Encyclopedia of Integer Sequences.

      Oct 22, 2015

      On the average summer Saturday, the mathematician Neil Sloane woke up to a crisis. “There are always crises,” he said— albeit crises of the teapot tempest variety. One Saturday over breakfast, he faced an inbox message titled “edits from outer space.

      10 min read

    • UNLIMITED

      A Universe Made of Tiny, Random Chunks: The space-time that makes up our universe is inherently uncertain.

      Jun 6, 2013

      One of science’s most crucial yet underappreciated achievements is the description of the physical universe using mathematics—in particular, using continuous, smooth mathematical functions, like how a sine wave describes both light and sound. This is

      6 min read

    • UNLIMITED

      Cloudy With a Chance of War

      Mar 7, 2019

      The burial detail, which had come for the corpses in the pigpen, was surprised. The “dead” were getting up and speaking English. Qu’est-ce que c’est? Ah, they were an ambulance crew. British volunteers, in the trenches with the French Army on the Wes

      14 min read

    • UNLIMITED

      Cloudy With a Chance of War: His weather forecasts changed the world. Could his predictions of war?

      Jul 31, 2014

      The burial detail, which had come for the corpses in the pigpen, was surprised. The “dead” were getting up and speaking English. Qu’est-ce que c’est? Ah, they were an ambulance crew. British volunteers, in the trenches with the French Army on the Wes

      14 min read

    • UNLIMITED

      The Sacred, Spherical Cows of Physics: Theoretical physics milks symmetry to power its newest tool.

      May 1, 2014

      Early in their training, many physics students come across the idea of spherical cows. Cows in the real world—even at their most plump and well-fed—are hardly spherical, and this makes it tricky to calculate things like, say, how their volume or surf

      11 min read

    • UNLIMITED

      Damion Searls

      Sep 15, 2019

      Joseph Moxon, Mechanick Exercises. Vol. 2 (1683–84), the first known manual of printing J. M. begins his book,Every thought taken up from the block with a rollOf the ball and inked on the form,A Craft of the Hand which cannot be taught by Words:“I th

      6 min read

    • UNLIMITED

      The Universe Began With a Big Melt, Not a Big Bang

      Oct 5, 2017

      There are two tantalizing mysteries about our universe, one dealing with its final fate and the other with its beginning, that have intrigued cosmologists for decades. The community has always believed these to be independent problems—but what if the

      10 min read

    • UNLIMITED

      How the Universe Remembers Information

      Feb 28, 2019

      It was one of the great missed connections of physics. In 1965 a particle theorist derived a formula for the collision of elementary particles. Twenty years later two gravitation theorists, using completely different techniques, derived a formula for

      6 min read

    • UNLIMITED

      Will Quantum Mechanics Swallow Relativity?

      Jun 8, 2017

      It is the biggest of problems, it is the smallest of problems. At present physicists have two separate rulebooks explaining how nature works. There is general relativity, which beautifully accounts for gravity and all of the things it dominates: orbi

      17 min read

    • UNLIMITED

      Will Quantum Mechanics Swallow Relativity?: The contest between gravity and quantum physics takes a new turn.

      Oct 29, 2015

      It is the biggest of problems, it is the smallest of problems. At present physicists have two separate rulebooks explaining how nature works. There is general relativity, which beautifully accounts for gravity and all of the things it dominates: orbi

      17 min read

    • UNLIMITED

      The Scientific Problem That Must Be Experienced: To understand turbulence we need the intuitive perspective of art.

      Jul 3, 2014

      When the German physicist Arnold Sommerfeld assigned his most brilliant student a subject for his doctoral thesis in 1923, he admitted that “I would not have proposed a topic of this difficulty to any of my other pupils.” Those others included such g

      16 min read

    • UNLIMITED

      Book Reviews

      Jun 4, 2020

      Book Reviews
      3 min read

    • UNLIMITED

      Book Reviews

      Mar 5, 2020

      Book Reviews
      3 min read

    • UNLIMITED

      Do We Have the Big Bang Theory All Wrong?: One physicist’s radical reinterpretation of the cosmic microwave background.

      Jul 31, 2014

      All that Hans-Jörg Fahr wants is for someone to prove him wrong. A professor of astrophysics at the University of Bonn in Germany, he has taken a stand against nearly the entire field of cosmology by claiming that the diffuse glow of background micro

      7 min read

    • UNLIMITED

      How to Weigh the World

      Mar 6, 2017

      How to Weigh the World
      4 min read

    • UNLIMITED

      A Letter to Einstein From the Future: Two Princeton Physicists Catch Albert Up.

      Sep 14, 2017

      We don’t believe in time travel, and we’re not into mysticism. But what if we could write a letter to Albert Einstein to tell him about gravity and black holes in a few paragraphs? We’d write something like this letter. Steven Gubser and Frans Pretor

      4 min read

    Related categories

    Reviews for Characteristic Classes. (AM-76), Volume 76

    4.5/5

    5 ratings0 reviews

    What did you think?

    Tap to rate

    Review must be at least 10 words

      Book preview

      Characteristic Classes. (AM-76), Volume 76 - John Milnor

      Enjoying the preview?
      Page 1 of 1