Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bivariant Versions of Algebraic Cobordism   We define four distinct oriented bivariant theories associated with algebraic
cobordism in its two versions (the axiomatic $\Omega$ and the geometric
$\omega$), when applied to quasi-projective varieties over a field $k$.
Specifically, we obtain contravariant analogues of the algebraic bordism group
$\Omega_*(X)$ and the double point bordism group $\omega_*(X)$, for $X$ a
quasi-projective variety, and covariant analogues of the algebraic cobordism
ring $\Omega^*(X)$ and the double point cobordism ring $\omega^*(X)$, for $X$ a
smooth variety. When the ground field has characteristic zero, we use the
universal properties of algebraic cobordism in order to obtain correspondences
between these oriented bivariant theories.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph