Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stiefel-Whitney classes and immersions of orientable and Spin manifolds   We determine a nice simple formula for the largest Euclidean space for which
there is an orientable n-manifold with a nonimmersion detected by
Stiefel-Whitney classes. For Spin manifolds, we prove the analogue of the upper
bound and establish the complete answer for n<24 and n=33,34. Results similar
to many of these were obtained some 50 years ago, but in a much less tractable
form. The sharp results for Spin manifolds require detailed calculations of
ko-homology groups of mod-2 Eilenberg-MacLane spaces.

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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys