Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quandle homotopy invariants of knotted surfaces   Given a finite quandle, we introduce a quandle homotopy invariant of knotted
surfaces in the 4-sphere, modifying that of classical links. This invariant is
valued in the third homotopy group of the quandle space, and is universal among
the (generalized) quandle cocycle invariants. We compute the second and third
homotopy groups, with respect to "regular Alexander quandles". As a corollary,
any quandle cocycle invariant using the dihedral quandle of prime order is a
scalar multiple of the Mochizuki 3-cocycle invariant. As another result, we
determine the third quandle homology group of the dihedral quandle of odd
order.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics