Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heegaard surfaces and the distance of amalgamation   Let $M_1$ and $M_2$ be orientable irreducible 3--manifolds with connected
boundary and suppose $\partial M_1\cong\partial M_2$. Let $M$ be a closed
3--manifold obtained by gluing $M_1$ to $M_2$ along the boundary. We show that
if the gluing homeomorphism is sufficiently complicated, then $M$ is not
homeomorphic to $S^3$ and all small-genus Heegaard splittings of $M$ are
standard in a certain sense. In particular, $g(M)=g(M_1)+g(M_2)-g(\partial
M_i)$, where $g(M)$ denotes the Heegaard genus of $M$. This theorem is also
true for certain manifolds with multiple boundary components.

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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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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: physics
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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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: cond-mat
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The categories of this paper are: stat