A constructive approach to higher homotopy operations

David Blanc, Mark W. Johnson, James M. Turner

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this paper we provide an explicit general construction of higher homotopy operations in model categories, which include classical examples such as (long) Toda brackets and (iterated) Massey products, but also cover unpointed operations not usually considered in this context. We show how such operations, thought of as obstructions to rectifying a homotopy-commutative diagram, can be defined in terms of a double induction, yielding intermediate obstructions as well.

Original languageEnglish
Title of host publicationHomotopy Theory
Subtitle of host publicationTools and Applications
EditorsDaniel G. Davis, Mark W. Johnson, Charles Rezk, Hans-Werner Henn, J. F. Jardine
PublisherAmerican Mathematical Society
Number of pages54
ISBN (Print)9781470442446
StatePublished - 2019
EventConference on Homotopy Theory: Tools and Applications, 2017 - Urbana, United States
Duration: 17 Jul 201721 Jul 2017

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


ConferenceConference on Homotopy Theory: Tools and Applications, 2017
Country/TerritoryUnited States

Bibliographical note

Funding Information:
0.1. Acknowledgements. We wish to thank the referee and editor for their detailed and pertinent comments. The research of the first author was supported by Israel Science Foundation grants 74/11 and 770/16, and the third author by National Science Foundation grant DMS-1207746.

Publisher Copyright:
© 2019 American Mathematical Society.


  • Higher homotopy operations
  • Homotopy-commutative diagram
  • Obstructions

ASJC Scopus subject areas

  • General Mathematics


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