Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sharp signature bound for positive four-braids   We provide the optimal linear bound for the signature of positive four-braids
in terms of the three-genus of their closures. As a consequence, we improve
previously known linear bounds for the signature in terms of the first Betti
number for all positive braid links. We obtain our results by combining bounds
for positive three-braids with Gordon and Litherland's approach to signature
via unoriented surfaces and their Goeritz forms. Examples of families of
positive four-braids for which the bounds are sharp are provided.

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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci