Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Untwisting information from Heegaard Floer homology   The unknotting number of a knot is the minimum number of crossings one must
change to turn that knot into the unknot. We work with a generalization of
unknotting number due to Mathieu-Domergue, which we call the untwisting number.
The p-untwisting number is the minimum number (over all diagrams of a knot) of
full twists on at most 2p strands of a knot, with half of the strands oriented
in each direction, necessary to transform that knot into the unknot. In
previous work, we showed that the unknotting and untwisting numbers can be
arbitrarily different. In this paper, we show that a common route for
obstructing low unknotting number, the Montesinos trick, does not generalize to
the untwisting number. However, we use a different approach to get conditions
on the Heegaard Floer correction terms of the branched double cover of a knot
with untwisting number one. This allows us to obstruct several 10 and
11-crossing knots from being unknotted by a single positive or negative twist.
We also use the Ozsv\'ath-Szab\'o tau invariant and the Rasmussen s invariant
to differentiate between the p- and q-untwisting numbers for certain p,q > 1.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con