If M is the complement of a hyperplane arrangement, and A = H(M, k) is the cohomology ring of M over a field of characteristic 0, then the ranks, φk, of the lower central series quotients of π1(M) can be computed from the Betti numbers, bii = dimTor A i (k, k)i, of the linear strand in a minimal free resolution of k over A. We use the Cartan-Eilenberg change of rings spectral sequence to relate...

The quotients Gk/Gk+1 of the lower central series of a finitely presented group G are an important invariant of this group. In this work we investigate the ranks of these quotients in the case of a certain class of conjugation-free groups, which are groups generated by x1, . . . , xn and having only cyclic relations: xitxit−1 · . . . · xi1 = xit−1 · . . . · xi1xit = · · · = xi1xit · . . . · xi2...

In this paper we study the lower central series {Li}i≥1 of algebras with polynomial identities. More specifically, we investigate the properties of the quotients Ni = Mi/Mi+1 of successive ideals generated by the elements Li. We give a complete description of the structure of these quotients for the free metabelian associative algebra A/(A[A,A][A,A]). With methods from Polynomial Identities the...

The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface Sg of genus g. Penner proved that the logarithm of the minimal dilatation for a pseudo-Anosov homeomorphism of Sg tends to zero at the rate 1/g. We consider here the smallest dilatation of any pseudoAnosov homeomorphism of Sg acting trivially on Γ/Γk, the quotie...

Let X and Y be finite-type CW–complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k–rescaling of the rational cohomology ring of X . Assume H∗(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra π∗(ΩY ) ⊗ Q equals, up to k–rescaling, the graded rational Lie algebra associated to the lower central series of π1(X). If Y is a formal space, this equali...