Lins-Mandel 3-manifolds and their groups: a simple proof of the homology sphere conjecture

The Lins-Mandel manifolds are combinatorially represented by a 4-parametric family of colored graphs S(n,\ell,t,c) defined in Discrete Math. 57 (1985). In the present paper we obtain a finite presentation of the fundamental group of such manifolds for t = \ell -1 and c=1. As a consequence, the homology sphere conjecture 2, stated in the quoted paper, can be easily proved by a direct algebraic calculus on the homology groups.