Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-solvable and two-bipolar knots with large four-genera   For every integer g, we construct a 2-solvable and 2-bipolar knot whose
topological 4-genus is greater than g. Note that 2-solvable knots are in
particular algebraically slice and have vanishing Casson-Gordon obstructions.
Similarly all known smooth 4-genus bounds from gauge theory and Floer homology
vanish for 2-bipolar knots. Moreover, our knots bound smoothly embedded height
four gropes in $D^4$, an a priori stronger condition than being 2-solvable. We
use new lower bounds for the 4-genus arising from $L^{(2)}$-signature defects
associated to meta-metabelian representations of the fundamental group.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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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: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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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: econ
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The categories of this paper are: nlin