Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transverse Surgery on Knots in Contact 3-Manifolds   We study the effect of surgery on transverse knots in contact 3-manifolds. In
particular, we investigate the effect of such surgery on open books, the
Heegaard Floer contact invariant, and tightness. The overarching theme of this
paper is to show that in many contexts, surgery on transverse knots is more
natural than surgery on Legendrian knots.
  Besides reinterpreting surgery on Legendrian knots in terms of transverse
knots, our main results on are in two complementary directions: conditions
under which inadmissible transverse surgery (\textit{cf.\@} positive contact
surgery on Legendrian knots) preserves tightness, and conditions under which it
creates overtwistedness. In the first direction, we give the first result on
the tightness of inadmissible transverse surgery for contact manifolds with
vanishing Heegaard Floer contact invariant. In particular, inadmissible
transverse surgery on the connected binding of a genus $g$ open book that
supports a tight contact structure preserves tightness if the surgery
coefficient is greater than $2g-1$. In the second direction, along with more
general statements, we deduce a partial generalisation to a result of Lisca and
Stipsicz: when $L$ is a Legendrian knot with $tb(L) \leq -2$, and $|rot(L)|
\geq 2g(L)+tb(L)$, then contact $(+1)$-surgery on $L$ is overtwisted.

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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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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: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con