On the Fundamental Group and Triple Massey’s Product

We study the relations between the fundamental group and the homological operations on integer homology. For the “rational” fundamental group (Malcev completion) see [2, 3, 4, 11, 16, 17]. This work is an attempt to understand the invariant of the fundamental group of the complement of a complex hyperplane arrangement that was used in [13]. Note that this invariant necessarily vanishes over Q (see [5]). All homology and cohomology groups are with integer coefficients. By |X | we denote the geometric realization of a simplicial set X .