Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Gromov-Hausdorff distance between spheres   We provide general upper and lower bounds for the Gromov-Hausdorff distance
$d_{\mathrm{GH}}(\mathbb{S}^m,\mathbb{S}^n)$ between spheres $\mathbb{S}^m$ and
$\mathbb{S}^n$ (endowed with the round metric) for $0\leq m< n\leq \infty$.
Some of these lower bounds are based on certain topological ideas related to
the Borsuk-Ulam theorem. Via explicit constructions of (optimal)
correspondences we prove that our lower bounds are tight in the cases of
$d_{\mathrm{GH}}(\mathbb{S}^0,\mathbb{S}^n)$,
$d_{\mathrm{GH}}(\mathbb{S}^m,\mathbb{S}^\infty)$,
$d_{\mathrm{GH}}(\mathbb{S}^1,\mathbb{S}^2)$,
$d_{\mathrm{GH}}(\mathbb{S}^1,\mathbb{S}^3)$ and
$d_{\mathrm{GH}}(\mathbb{S}^2,\mathbb{S}^3)$. We also formulate a number of
open questions.

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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: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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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: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-lat