Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Virtual pullbacks in $K$-theory   We consider virtual pullbacks in $K$-theory, and show that they are bivariant
classes and satisfy certain functoriality. As applications to $K$-theoretic
counting invariants, we include proofs of a virtual localization formula for
schemes and a degeneration formula in Donaldson-Thomas theory.

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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph