Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A K-theoretic refinement of topological realization of unstable algebras   In this paper we propose and partially carry out a program to use $K$-theory
to refine the topological realization problem of unstable algebras over the
Steenrod algebra. In particular, we establish a suitable form of algebraic
models for $K$-theory of spaces, called $\psi^p$-algebras, which give rise to
unstable algebras by taking associated graded algebras mod $p$. The
aforementioned problem is then split into (i) the \emph{algebraic} problem of
realizing unstable algebras as mod $p$ associated graded of $\psi^p$-algebras
and (ii) the \emph{topological} problem of realizing $\psi^p$-algebras as
$K$-theory of spaces. Regarding the algebraic problem, a theorem shows that
every connected and even unstable algebra can be realized. We tackle the
topological problem by obtaining a $K$-theoretic analogue of a theorem of Kuhn
and Schwartz on the so-called Realization Conjecture.

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The categories of this paper are: acc-phys
28
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: patt-sol
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
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The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat