Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Kontsevich's characteristic classes for smooth 5- and 7-dimensional
  homology sphere bundles   M. Kontsevich constructed universal characteristic classes of smooth bundles
with fiber a framed odd-dimensional integral homology sphere. In dimension 3,
they are known to give a universal finite type invariants of homology
3-spheres. However, they have not been well understood for higher fiber
dimensions. The purpose of the present paper is twofold. First, we obtain a
bordism invariant of smooth unframed bundles with fiber a 5-dimensional
homology sphere, which is defined as a sum of the simplest Kontsevich class and
the second signature defect. It may be in some sense a higher dimensional
analogue of the Casson invariant. Second, we construct a family of M-bundles.
By evaluating on those M-bundles, we show that Kontsevich's universal
characteristic classes are highly non-trivial in the case of fiber dimension 7.
As a corollary, new estimates for unstable rational homotopy groups of
Diff(D^7,\partial D^7) are obtained.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th