Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correction to "Toroidal and Klein bottle boundary slopes"   Let M be a compact, connected, orientable, irreducible 3-manifold and T an
incompressible torus boundary component of M such that the pair (M,T) is not
cabled. In the paper "Toroidal and Klein bottle boundary slopes"
[arXiv:math/0601034] by the author it was established that for any
K-incompressible tori F,F' in (M,T) which intersect in graphs G in F and G' in
F', the maximal number of mutually parallel, consecutive, negative edges that
may appear in G is n'+1, where n' is the number of boundary components of F'.
In this paper we show that the correct such bound is n'+2, give a partial
classification of the pairs (M,T) where the bound n'+2 is reached, and show
that if the distance d between the boundary slopes of F and F' is at least 6
then the bound n'+2 cannot be reached; this latter fact allows for the short
proof of the classification of the pairs (M,T) with M a hyperbolic 3-manifold
and d at least 6 to work without change as outlined in the paper cited above.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an