Moduli spaces for fundamental groups and link invariants derived from the lower central series
Let spaces be connected with finite Betti numbers. The authors construct algebraic parametrizations of the Maltsev completed fundamental groups \(\pi_ 1(S)\) of spaces \(S\) with prescribed first and second Betti number. The nilpotent version parametrizes the groups \(\pi_ 1 (S)/ \Gamma_ k (\pi_ 1(S))\otimes \mathbb{Q}\) (where \(\Gamma_ k\) denotes the \(k\)-th term of the lower central series). The ``moduli space'' of corresponding isomorphism classes is the orbit set of a (pro)unipotent group. The method is related to Chen's iterated integral approach to \(\pi_ 1\). It is shown that these invariants are well accessible to computations. The main applications are to link theory as is well illustrated by theorems and many examples. A rigidity theorem for \(\text{gr} (\pi_ 1 (S)) \otimes\mathbb{Q}\) is also given.
spaces with prescribed first and second Betti number
scientific article; zbMATH DE number 554382
scientific article