Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Examples of biquotients whose tangent bundle is not a biquotient vector
  bundle   A biquotient vector bundle is any vector bundle over a biquotient $G/\!\!/H$
of the form $G \times_H V$ for an $H$-representation $V$. In this article, we
study the question of when the tangent bundle of $G/\!\!/H$ is a biquotient
vector bundle. We find infinite families of examples of biquotients $M =
G/\!\!/H$ for which the tangent bundle is not a biquotient vector bundle for
any presentation of $M$ as a biquotient. In addition, we find infinite families
of examples for which $TM$ is or is not a biquotient vector bundle depending on
the presentation of $M$ as a biquotient. Finally, an appendix by Michael
Albanese contains a proof of an unpublished result of Hirzebruch.

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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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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: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: physics