ISSN:
1432-1297
Keywords:
55P62
;
55M30
;
55P35
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetR S (resp.R A) be the radius of convergence of the Poincaré series of a loop space Ω(S) (resp. of the Betti-Poincaré 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 p H $$(\mathbb{K},\mathbb{K})$$ grows exponentially withp.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01394059
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