Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of knotted tori in the 2-metastable dimension   This paper is on the classical Knotting Problem: for a given manifold N and a
number m describe the set of isotopy classes of embeddings N->S^m. We study the
specific case of knotted tori, i. e. the embeddings S^p x S^q -> S^m. The
classification of knotted tori up to isotopy in the metastable dimension range
m>p+3q/2+3/2, p<q+1, was given by A. Haefliger, E. Zeeman and A. Skopenkov. We
consider the dimensions below the metastable range, and give an explicit
criterion for the finiteness of this set of isotopy classes in the 2-metastable
dimension:
  Theorem. Assume that p+4q/3+2<m<p+3q/2+2 and m>2p+q+2. Then the set of smooth
embeddings S^p x S^q -> S^m up to isotopy is infinite if and only if either q+1
or p+q+1 is divisible by 4.
  Our approach to the classification is based on an analogue of the Koschorke
exact sequence from the theory of link maps. This sequence involves a new
beta-invariant of knotted tori. The exactness is proved using embedded surgery
and the Habegger-Kaiser techniques of studying the complement.

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The categories of this paper are: cs
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The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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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-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th