Planar Algebra
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In more detail, give a list of words w_1, w_2, ldots, w_k, and a single word w0, we define a tangle from (w_1, w_2, dots, w_k) to w0 to be a disk D in the plane, with points around its circumference labelled in order by the letters of w0, with k internal disks removed, indexed 1 through k, with the i-th internal disk having points around its circumference labelled in order by the letters of wi, and finally, with a collection of oriented non-intersecting curves lying i...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In more detail, give a list of words w_1, w_2, ldots, w_k, and a single word w0, we define a tangle from (w_1, w_2, dots, w_k) to w0 to be a disk D in the plane, with points around its circumference labelled in order by the letters of w0, with k internal disks removed, indexed 1 through k, with the i-th internal disk having points around its circumference labelled in order by the letters of wi, and finally, with a collection of oriented non-intersecting curves lying in the remaining portion of the disk, with each component being labelled by an element of the label set, such that the set of end points of these curves coincide exactly with the labelled points on the internal and external circumferences, and at the initial points of the curves, the label on the curves coincides with the label on the circumference, while at the final points, the label on thecurve coincides with the involute of the label on the circumference. While this sounds complicated, an illustrated example does wonders!
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