The radius of convergence of Poincar� series of loop spaces
Copyright policy )The radius of convergence of Poincar� series of loop spaces
LetR S (resp.R A) be the radius of convergence of the Poincare series of a loop space Ω(S) (resp. of the Betti-Poincare series of a noetherian connected graded commutative algebraA over a field $$\mathbb{K}$$ of characteristic zero). IfS is a finite 1-connected CW-complex, the rational homotopy Lie algebra ofS is finite dimensional if and only ifR S-1. OtherwiseR S<1. There is an easily computable upper bound (usually less than 1) forR S ifS is formal or coformal. On the other handR A=+∞ if and only ifA is a polynomial algebra andR A=1 if and only ifA is a complete intersection (Golod and Gulliksen conjecture). OtherwiseR A<1 and the sequence dim Tor $$(\mathbb{K},\mathbb{K})$$ grows exponentially withp.
- Université Catholique de Louvain Belgium
- DigiZeitschriften Germany
Betti- Poincare series of a noetherian connected graded commutative algebra, Rational homotopy theory, rational homotopy Lie algebra of a finite 1-connected CW-complex, formal and coformal spaces, Graded rings and modules (associative rings and algebras), Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects), Lusternik-Schnirelmann category, Article, Poincare-Koszul series, 510.mathematics, Complete intersections, polynomial algebra, complete intersection, Loop spaces, radius of convergence of the Poincare series of a loop space
Betti- Poincare series of a noetherian connected graded commutative algebra, Rational homotopy theory, rational homotopy Lie algebra of a finite 1-connected CW-complex, formal and coformal spaces, Graded rings and modules (associative rings and algebras), Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects), Lusternik-Schnirelmann category, Article, Poincare-Koszul series, 510.mathematics, Complete intersections, polynomial algebra, complete intersection, Loop spaces, radius of convergence of the Poincare series of a loop space
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