Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Split Milnor-Witt Motive and its Application to Fiber Bundles   We study the Milnor-Witt motives which are a finite direct sum of
$\mathbb{Z}(q)[p]$ and $\mathbb{Z}/\eta(q)[p]$. We show that for MW-motives of
this type, we could determine an MW-motivic cohomology class in terms of a
motivic cohomology class and a Witt cohomology class. We define the motivic
Bockstein cohomology and show that it corresponds to subgroup of Witt
cohomology, if the MW-motive splits as above. As an application, we give the
splitting formula of Milnor-Witt motives of Grassmannian bundles and complete
flag bundles. This in particular shows that the integral cohomology of real
complete flags has only 2-torsions.

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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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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: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con