Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-type invariants of three-manifolds and the dimension subgroup
  problem   For a certain class of compact oriented 3-manifolds, M. Goussarov and K.
Habiro have conjectured that the information carried by finite-type invariants
should be characterized in terms of ``cut-and-paste'' operations defined by the
lower central series of the Torelli group of a surface.
  In this paper, we observe that this is a variation of a classical problem in
group theory, namely the ``dimension subgroup problem.'' This viewpoint allows
us to prove, by purely algebraic methods, an analogue of the Goussarov-Habiro
conjecture for finite-type invariants with values in a fixed field. We deduce
that their original conjecture is true at least in a weaker form.

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The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ