following is an example of a transparent disk:
D
tr
=
for
X
=
(5.23)
By definition, all defect lines of a transparent disk
D
tr
of type
A
are labeled by the trans-
parent defect label
I
0
=
A
for one and the same tensor category
A
. The framing of a fillable
disk
D
X
has the following property: since by definition every inner gluing segment is fillable by
a disk, the indices on the outer boundary
∂
outer
D
X
must add up to the value 2 (thus
∂
outer
D
X
is
not fillable). Moreover, the label of every defect line of
X
appears an even number of times as a
label of a defect point on
∂
D
X
. (The latter criteria are, however, not sufficient for the existence
of a fillable disk with a given boundary: If the cyclically ordered string of bimodules for the
boundary
∂
X
contains a string (
M
,
N
,
M
,
N
) with generic bimodules
M
and
N
, then there
does not exist a corresponding fillable disk.)
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- Fall '17
