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.
|Title of host publication||Homotopy Theory|
|Subtitle of host publication||Tools and Applications|
|Editors||Daniel G. Davis, Mark W. Johnson, Charles Rezk, Hans-Werner Henn, J. F. Jardine|
|Publisher||American Mathematical Society|
|Number of pages||54|
|State||Published - 2019|
|Event||Conference on Homotopy Theory: Tools and Applications, 2017 - Urbana, United States|
Duration: 17 Jul 2017 → 21 Jul 2017
|Conference||Conference on Homotopy Theory: Tools and Applications, 2017|
|Period||17/07/17 → 21/07/17|
Bibliographical noteFunding 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.
© 2019 American Mathematical Society.
- Higher homotopy operations
- Homotopy-commutative diagram
ASJC Scopus subject areas
- Mathematics (all)