Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic cycles and the classical groups II: Quaternionic cycles   In part I of this work we studied the spaces of real algebraic cycles on a
complex projective space P(V), where V carries a real structure, and completely
determined their homotopy type. We also extended some functors in K-theory to
algebraic cycles, establishing a direct relationship to characteristic classes
for the classical groups, specially Stiefel-Whitney classes. In this sequel, we
establish corresponding results in the case where V has a quaternionic
structure. The determination of the homotopy type of quaternionic algebraic
cycles is more involved than in the real case, but has a similarly simple
description. The stabilized space of quaternionic algebraic cycles admits a
nontrivial infinite loop space structure yielding, in particular, a delooping
of the total Pontrjagin class map. This stabilized space is directly related to
an extended notion of quaternionic spaces and bundles (KH-theory), in analogy
with Atiyah's real spaces and KR-theory, and the characteristic classes that we
introduce for these objects are nontrivial. The paper ends with various
examples and applications.

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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: supr-con