© 2020

Topology and K-Theory

Lectures by Daniel Quillen


Part of the Lecture Notes in Mathematics book series (LNM, volume 2262)

Also part of the History of Mathematics Subseries book sub series (HISTORYMS, volume 2262)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Robert Penner
    Pages 1-4
  3. Robert Penner
    Pages 5-8
  4. Robert Penner
    Pages 9-13
  5. Robert Penner
    Pages 15-19
  6. Robert Penner
    Pages 21-24
  7. Robert Penner
    Pages 25-31
  8. Robert Penner
    Pages 39-44
  9. Robert Penner
    Pages 45-49
  10. Robert Penner
    Pages 51-55
  11. Robert Penner
    Pages 57-60
  12. Robert Penner
    Pages 61-65
  13. Robert Penner
    Pages 67-70
  14. Robert Penner
    Pages 71-74
  15. Robert Penner
    Pages 75-82
  16. Robert Penner
    Pages 83-88
  17. Robert Penner
    Pages 89-93
  18. Robert Penner
    Pages 95-100
  19. Robert Penner
    Pages 101-103

About this book


These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980. He had just received the Fields Medal for his work on these topics among others and was funny and playful with a confident humility from the start. These are not meant to be polished lecture notes, rather, things are presented as did Quillen reflected in the hand-written notes, resisting any temptation to change or add notation, details or elaborations.  Indeed, the text is faithful to Quillen's own exposition, even respecting the {\sl board-like presentation} of formulae, diagrams and proofs, omitting numbering theorems in favor of names and so on. This is meant to be Quillen on Quillen as it happened forty years ago, an informal text for a second-semester graduate student on topology, category theory and K-theory, a potential preface to studying Quillen's own landmark papers and an informal glimpse of his great mind. The intellectual pace of the lectures, namely fast and lively, is Quillen himself, and part of the point here is to capture some of this intimacy. To be sure, much has happened since then from this categorical perspective started by Grothendieck, and Misha Kapranov has contributed an Afterword in order to make it more useful to current students.


Topology K-Theory Algebraic Topology Category Theory Homological Algebra Quillen K-Theory

Authors and affiliations

  1. 1.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance

About the authors

Robert Penner holds the Rene Thom Chair at the Institut des Hautes Etudes Scientifiques in Paris. His research extends across topology, geometry and combinatorics together with their applications to high energy physics and theoretical biology.  Among his previous books are
Combinatorics of Train Tracks (Princeton University Press), Discrete Mathematics (World Scientific) and Decorated Teichmueller Theory
(European Mathematical Society).

Bibliographic information