Algebra + homotopy = operad. (English) Zbl 1335.18001
Eguchi, Tohru (ed.) et al., Symplectic, Poisson, and noncommutative geometry. Selected papers based on the presentations at the conferences: conference on symplectic and Poisson geometry in interaction with analysis, algebra and topology, Berkeley, CA, USA, May 4–7, 2010, conference on symplectic geometry, noncommutative geometry and physics, Berkeley, CA, USA, May 10–14, 2010 and Kyoto, Japan, November 1–5, 2010. Cambridge: Cambridge University Press (ISBN 978-1-107-05641-1/hbk). Mathematical Sciences Research Institute Publications 62, 229-290 (2014).
Summary: This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher homotopies. We try to show how universal this theory is by giving many applications in algebra, geometry, topology, and mathematical physics. (This text is accessible to any student knowing what tensor products, chain complexes, and categories are.)
For the entire collection see [Zbl 1320.53003].
For the entire collection see [Zbl 1320.53003].
MSC:
| 18-02 | Research exposition (monographs, survey articles) pertaining to category theory |
| 55-02 | Research exposition (monographs, survey articles) pertaining to algebraic topology |
| 18D50 | Operads (MSC2010) |
| 16E45 | Differential graded algebras and applications (associative algebraic aspects) |
| 17B55 | Homological methods in Lie (super)algebras |
| 55P48 | Loop space machines and operads in algebraic topology |
