Moduli spaces for fundamental groups and link invariants derived from the lower central series
type: Item
instance of: scholarly article
title: Moduli spaces for fundamental groups and link invariants derived from the lower central series
zbMATH Open document ID: 0811.55008
DOI: 10.1007/BF02567856
author: Martin Markl
author: Ştefan Papadima
published in: Manuscripta Mathematica
publication date: 1995-05-02T00:00:00Z
full work available at URL: https://eudml.org/doc/155898
review text: 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.
reviewed by: Hans Scheerer
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 554382
zbMATH Keywords: spaces with prescribed first and second Betti number
zbMATH Keywords: classical links
zbMATH Keywords: Maltsev completed fundamental groups
zbMATH Keywords: iterated integral
zbMATH Keywords: link theory
MaRDI profile type: Publication
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OpenAlex ID: W2033228477
description: scientific article; zbMATH DE number 554382