Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy automorphisms of R-module bundles, and the K-theory of string
  topology   Let $R$ be a ring spectrum and $ E\to X$ an $R$-module bundle of rank $n$.
Our main result is to identify the homotopy type of the group-like monoid of
homotopy automorphisms of this bundle, $hAut^R(E)$. This will generalize the
result regarding $R$-line bundles previously proven by the authors. The main
application is the calculation of the homotopy type of $BGL_n(End ((L))$ where
$L \to X$ is any $R$-line bundle, and $End (L)$ is the ring spectrum of
endomorphisms. In the case when such a bundle is the fiberwise suspension
spectrum of a principal bundle over a manifold, $G \to P \to M$, this leads to
a description of the $K$-theory of the string topology spectrum in terms of the
mapping space from $M$ to $BGL (\Sigma^\infty (G_+))$.

4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga