Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stein traces and characterizing slopes   We show that there exists an infinite family of pairwise non-isotopic
Legendrian knots in the standard contact 3-sphere whose Stein traces are
equivalent. This is the first example of such phenomenon. Different
constructions are developed in the article, including a contact annulus twist,
explicit Weinstein handlebody equivalences, and a discussion on dualizable
patterns in the contact setting. These constructions can be used to
systematically construct distinct Legendrian knots in the standard contact
3-sphere with contactomorphic (-1)-surgeries and, in many cases, equivalent
Stein traces. In addition, we also discuss characterizing slopes and provide
results in the opposite direction, i.e. describe cases in which the Stein
trace, or the contactomorphism type of an r-surgery, uniquely determines the
Legendrian isotopy type.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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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: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom