4 research outputs found
Abe homotopy classification of topological excitations under the topological influence of vortices
Topological excitations are usually classified by the th homotopy group
. However, for topological excitations that coexist with vortices, there
are case in which an element of cannot properly describe the charge of
a topological excitation due to the influence of the vortices. This is because
an element of corresponding to the charge of a topological excitation
may change when the topological excitation circumnavigates a vortex. This
phenomenon is referred to as the action of on . In this paper,
we show that topological excitations coexisting with vortices are classified by
the Abe homotopy group . The th Abe homotopy group is
defined as a semi-direct product of and . In this framework, the
action of on is understood as originating from noncommutativity
between and . We show that a physical charge of a topological
excitation can be described in terms of the conjugacy class of the Abe homotopy
group. Moreover, the Abe homotopy group naturally describes vortex-pair
creation and annihilation processes, which also influence topological
excitations. We calculate the influence of vortices on topological excitations
for the case in which the order parameter manifold is , where is
an -dimensional sphere and is a discrete subgroup of . We show
that the influence of vortices on a topological excitation exists only if
is even and includes a nontrivial element of .Comment: 36 pages, 12 figure
Retroperitoneal lipoma arising from the urinary bladder
Retroperitoneal benign lipomas are extremely rare and represent about 2.9% of all primary retroperitoneal tumors. About 80% of the tumors in the retroperitoneal cavities are malignant neoplasms. We experienced a case of a retroperitoneal lipoma simulating an ovarian mature cystic teratoma. A diagnosis was correctly made by magnetic resonance imaging (MRI) prior to surgery, and a total tumorectomy was performed. The retroperitoneal lipoma was recognized to have arisen from the urinary bladder. Histological sections revealed a tumor consisting of typical adipose cells without atypia. These types of lipomas should be carefully followed-up because they often recur and undergo malignant transformations