Higher-order Alexander invariants of plane algebraic curves

C. Leidy, L. Maxim
2006 International mathematics research notices  
We define new higher-order Alexander modules A n (C) and higher-order degrees δ n (C) which are invariants of the algebraic planar curve C. These come from analyzing the module structure of the homology of certain solvable covers of the complement of the curve C. These invariants are in the spirit of those developed by T. Cochran in [2] and S. Harvey in [8] and [9] , which were used to study knots, 3-manifolds, and finitely presented groups, respectively. We show that for curves in general
more » ... ion at infinity, the higherorder degrees are finite. This provides new obstructions on the type of groups that can arise as fundamental groups of complements to affine curves in general position at infinity.
doi:10.1155/imrn/2006/12976 fatcat:7jk4w5rgi5cpxc7cbkfsvklzsy