Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new invariant and parametric connected sum of embeddings   We define an isotopy invariant of embeddings N -> R^m of manifolds into
Euclidean space. This invariant together with the \alpha-invariant of
Haefliger-Wu is complete in the dimension range where the \alpha-invariant
could be incomplete. We also define parametric connected sum of certain
embeddings (analogous to surgery). This allows to obtain new completeness
results for the \alpha-invariant and the following estimation of isotopy
classes of embeddings.
  For the piecewise-linear category, a (3n-2m+2)-connected n-manifold N and
(4n+4)/3 < m < (3n+3)/2 each preimage of \alpha-invariant injects into a
quotient of H_{3n-2m+3}(N), where the coefficients are Z for m-n odd and Z_2
for m-n even.

10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph