© 2017

Algebraic Topology

VIASM 2012–2015

  • H.V. Hưng Nguyễn
  • Lionel Schwartz


  • Provides self-contained, introductory texts to some advanced topics in modern algebraic topology

  • Includes various topics in homotopical algebra and stable homotopy

  • Leads quickly to open and concrete problems


Part of the Lecture Notes in Mathematics book series (LNM, volume 2194)

Table of contents

About this book


Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G. Ginot, H.-W. Henn and G. Powell. They are all introductory texts and can be used by PhD students and experts in the field. 

 Among the three contributions, two concern stable homotopy of spheres: Henn focusses on the chromatic point of view, the Morava K(n)-localization and the cohomology of the Morava stabilizer groups. Powell’s chapter is concerned with the derived functors of the destabilization and iterated loop functors and provides a small complex to compute them. Indications are given for the odd prime case.
Providing an introduction to some aspects of string and brane topology, Ginot’s contribution focusses on Hochschild homology and its generalizations. It contains a number of new results and fills a gap in the literature. 


String Topology Hochschild Homology Stable Homotopy of Spheres Morava K-theory Iterated Loop Functors 55P50,55Q45,55S10,18GXX. Nguyen H.V. Hung Nguyen

Editors and affiliations

  • H.V. Hưng Nguyễn
    • 1
  • Lionel Schwartz
    • 2
  1. 1.Department of MathematicsVietnam National UniversityHanoiVietnam
  2. 2.LAGA, UMR 7539 CNRS Institut GaliléeUniversité Paris 13VilletaneuseFrance

Bibliographic information

  • Book Title Algebraic Topology
  • Book Subtitle VIASM 2012–2015
  • Editors H.V. Hưng Nguyễn
    Lionel Schwartz
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-69433-7
  • eBook ISBN 978-3-319-69434-4
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VII, 180
  • Number of Illustrations 3 b/w illustrations, 2 illustrations in colour
  • Topics Algebraic Topology
    Category Theory, Homological Algebra
  • Buy this book on publisher's site