Through the looking glass: A dictionary between rational homotopy theory and local algebra. (English) Zbl 0588.13010

Avramov, Luchezar; Halperin, Stephen

Algebra, algebraic topology and their interactions, Proc. Conf., Stockholm 1983, Lect. Notes Math. 1183, 1-27 (1986).

[For the entire collection see Zbl 0577.00005.]
Since the paper by J.-E. Roos in Sémin. d’algèbre P. Dubreil, Proc., Paris 1977/78, Lect. Notes Math. 740, 285-322 (1979; Zbl 0415.13012) there has been an intense study on the analogy between rational homotopy theory in topology and homology of local rings in algebra. This paper is written by two of the main contributors to this study. It contains an overview of old and new results and a dictionary on the interplay between the two subjects.

Reviewer: R.Fröberg

MSC:

13D03	(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13H99	Local rings and semilocal rings
13-02	Research exposition (monographs, survey articles) pertaining to commutative algebra
55-02	Research exposition (monographs, survey articles) pertaining to algebraic topology
55P62	Rational homotopy theory

Keywords:

loop space; Poincaré series; DGA-algebra; analogy between rational homotopy theory in topology and homology of local rings in algebra.; dictionary

Citations:

Zbl 0577.00005; Zbl 0415.13012