Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pontrjagin forms and invariant objects related to the Q-curvature   We clarify the conformal invariance of the Pontrjagin forms by giving them a
manifestly conformally invariant construction; they are shown to be the
Pontrjagin forms of the conformally invariant tractor connection. The
Q-curvature is intimately related to the Pfaffian. Working on even-dimensional
manifolds, we show how the $k$-form operators $Q_k$ of \cite{ddd}, which
generalise the Q-curvature, retain a key aspect of the $Q$-curvature's relation
to the Pfaffian, by obstructing certain representations of natural operators on
closed forms. In a closely related direction, we show that the $Q_k$ give rise
to conformally invariant quadratic forms $\Theta_k$ on cohomology that
interpolate, in a suitable sense, between the integrated metric pairing (at
$k=n/2$) and the Pfaffian (at $k=0$). Using a different construction, we show
that the $Q_k$ operators yield a generalisation of the period map which maps
conformal structures to Lagrangian subspaces of the direct sum $H^k\oplus H_k$
(where $H_k$ is the dual of the de Rham cohomology space $H^k$). We couple the
$Q_k$ operators with the Pontrjagin forms to construct new natural densities
that have many properties in common with the original Q-curvature; in
particular these integrate to global conformal invariants. We also work out a
relevant example, and show that the proof of the invariance of the (nonlinear)
action functional whose critical metrics have constant Q-curvature extends to
the action functionals for these new Q-like objects. Finally we set up
eigenvalue problems that generalise to $Q_k$-operators the Q-curvature
prescription problem.

37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin