Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable and Unstable operations in Algebraic Cobordism   We describe additive (unstable) operations from a theory A^* obtained from
Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any
oriented cohomology theory B^*. We prove that there is 1-to-1 correspondence
between the set of operations, and the set of transformations:
A^n((P^{\infty})^{\times r}) ---> B^m((P^{\infty})^{\times r}) satisfying
certain simple properties. This provides an effective tool of constructing such
operations. As an application, we prove that (unstable) additive operations in
Algebraic Cobordism are in 1-to-1 correspondence with the L\otimes_Z Q-linear
combinations of Landweber-Novikov operations which take integral values on the
products of projective spaces. On our way we obtain that stable operations
there are exactly L-linear combinations of Landweber-Novikov operations. We
also show that multiplicative operations A^* ---> B^* are in 1-to-1
correspondence with the morphisms of the respective formal group laws. We
construct Integral (!) Adams Operations in Algebraic Cobordism, and all
theories obtained from it by change of coefficients, giving classical Adams
operations in the case of K_0. Finally, we construct Symmetric Operations for
all primes p (these operations in Algebraic Cobordism, previously known only
for p=2, are more subtle than the Landweber-Novikov operations, and have
applications to rationality questions), as well as the T.tom Dieck - style
Steenrod operations in Algebraic Cobordism. As a bi-product of the proof of our
main theorem we get the Riemann-Roch Theorem for additive (unstable)
operations.

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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th