Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Influence of topological constraints and topological excitations:
  Decomposition formulas for calculating homotopy groups of symmetry-broken
  phases   A symmetry broken phase of a system with internal degrees of freedom often
features a complex order parameter, which generates a rich variety of
topological excitations and imposes topological constraints on their
interaction (topological influence); yet the very complexity of the order
parameter makes it difficult to treat topological excitations and topological
influence systematically. To overcome this problem, we develop a general method
to calculate homotopy groups and derive decomposition formulas which express
homotopy groups of the order parameter manifold $G/H$ in terms of those of the
symmetry $G$ of a system and those of the remaining symmetry $H$ of the state.
By applying these formulas to general monopoles and three-dimensional
skyrmions, we show that their textures are obtained through substitution of the
corresponding $\mathfrak{su}(2)$-subalgebra for the $\mathfrak{su}(2)$-spin. We
also show that a discrete symmetry of $H$ is necessary for the presence of
topological influence and find topological influence on a skyrmion
characterized by a non-Abelian permutation group of three elements in the
ground state of an SU(3)-Heisenberg model.

15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org