Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: HL-homotopy of handlebody-links and Milnor's invariants   A handlebody-link is a disjoint union of embeddings of handlebodies in $S^3$
and an HL-homotopy is an equivalence relation on handlebody-links generated by
self-crossing changes. The second author and Ryo Nikkuni classified the set of
HL-homotopy classes of 2-component handlebody-links completely using the
linking numbers for handlebody-links. In this paper, we construct a family of
invariants for HL-homotopy classes of general handlebody-links, by using
Milnor's link-homotopy invariants. Moreover, we give a bijection between the
set of HL-homotopy classes of almost trivial handlebody-links and tensor
product space modulo some general linear actions, especially for 3- or more
component handlebody-links. Through this bijection we construct comparable
invariants of HL-homotopy classes.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics