On the asphericity of certain relative presentations over torsion-free groups

초록

It is noteworthy to find whether a relative presentation with torsion-free coefficients is aspherical or not, since a nonaspherical relative presentation that defines a torsion-free group would provide a potential counterexample to the Kaplansky zero-divisor conjecture, see [7]. In this paper we investigate asphericity of the relative group presentation < H, x : x(m1)h(1)x(m2)h(2) ... x(mk)h(k)> provided that m(1), m(2),..., m(k) are nonzero integers, k <= 3, each coefficient has infinite order and the relator is not a proper power.

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