In the answer to [MO question 132247](https://mathoverflow.net/questions/132247/quotient-groups-of-the-lower-central-series-of-a-free-group/132253), it is possible to find a nice computation of the quotient groups of the lower central series of a finitely generated free group. 



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> **Q.** What are the quotient groups of the lower central series of the genus $g$ surface group $\Pi\_g$, namely $$\Pi\_g = \langle a\_1, \ldots, a\_g, \, b\_1, \ldots, b\_g \; | \; [a\_1, \, b\_1] \cdots [a\_g, \, b\_g]=1 \rangle?$$ 
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I guess that it is a very classical subject with a huge literature, but I am not an expert in the area, so any pointer to some relevant book/article will be higly appreciated. 



Quotient groups of the lower central series of a surface group
This paper seems to be relevant: 


* S. Papadima and S. Yuzvinsky. On rational $K[π,1]$ spaces and Koszul algebras. J. Pure Appl. Algebra 144 (1999), no. 2, 157–167. [(link to paper on ScienceDirect)](https://www.sciencedirect.com/science/article/pii/S0022404998000589)


At least it contains the formula for dimenions in terms of Betti numbers mentioned in grok's answer to [the MO-question](https://mathoverflow.net/questions/87160/) I pointed out in the comments. There is a significant amount of further literature related to associated Lie algebras, Malcev completion of fundamental groups, Koszul duality properties and Chen's iterated integral. (You can either start browsing using these keywords, or start with papers coauthored by Papadima or Suciu and work through the references. I could also provide some more references if you state more precisely what type of answer you are looking for.) 


Maybe on a historic note, it seems that the subquotients for the lower central series of one-relator groups were first computed by Labute (but this doesn't involve the Koszul point of view, rather the relation to the lower central series for free groups).


* J.P. Labute. On the descending central series of groups with a single defining relation. J. Algebra 14 1970 16–23.


