ON n-DEFICIENCY OF GROUPS

초록

Let G be a group of type F(n) with n >= 2, i.e. G admits a finite n-dimensional (n - 1)-aspherical CW-complex X such that pi(1)(X) is isomorphic to G. We introduce the notion of the n-deficiency d(n)(G) which is a generalized notion of deficiency of G and present various results about the relation between d(n)(G) and the L(2)-Betti numbers of G. We also give some partial results about the Eilenberg-Ganea conjecture and the Whitehead conjecture. These results correspond to a generalization of several earlier results [Quart. J. Math. Oxford (2) 38 (1987) 35-44; J. Pure Appl. Algebra 7 (1976) 241-248; Quart. J. Math. Oxford (2) 32 (1981) 45-55; 2-Knots and Their Groups (Cambridge University Press, 1989)].

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