Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torsion and fibrations   We study the behaviour of analytic torsion under smooth fibrations. Namely,
let F \to E \to^{f} B be a smooth fiber bundle of connected closed oriented
smooth manifolds and let $V$ be a flat vector bundle over $E$. Assume that $E$
and $B$ come with Riemannian metrics and $V$ comes with a unimodular (not
necessarily flat) Riemannian metric. Let $\rho_{an}(E;V)$ be the analytic
torsion of $E$ with coefficients in $V$ and let $\Pf_B$ be the Pfaffian
$\dim(B)$-form. Let $H^q_{dR}(F;V)$ be the flat vector bundle over $B$ whose
fiber over $b \in B$ is $H^q_{dR}(F_b;V)$ with the Riemannian metric which
comes from the Hilbert space structure on the space of harmonic forms induced
by the Riemannian metrics. Let $\rho_{an}(B;H^q_{dR}(F;V))$ be the analytic
torsion of $B$ with coefficients in this bundle. The Leray-Serre spectral
sequence for deRham cohomology determines a certain correction term
$\rho^{Serre}_{dR}(f)$. We prove $\rho_{an}(E;V) = \int_B \rho_{an}(F_b;V)
\cdot \Pf_B + \sum_{q} (-1)^q \cdot \rho_{an}(B;H^q_{dR}(F;V)) +
\rho^{Serre}_{dR}(f)$.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org