Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On invariants and homology of spaces of knots in arbitrary manifolds   Finite-order invariants of knots in arbitrary 3-manifolds (including
non-orientable ones) are constructed and studied by methods of the topology of
discriminant sets. Obstructions to the integrability of admissible weight
systems to well-defined knot invariants are identified as 1-dimensional
cohomology classes of generalized loop spaces of the manifold. Unlike the case
of the 3-sphere, these obstructions can be non-trivial and provide invariants
of the manifold itself.
  The corresponding algebraic machinery allows us to obtain on the level of the
``abstract nonsense'' some of results and problems of the theory, and to
extract from other the essential topological part.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg