I'm currently reading through Bakalov and Kirillov's "Lectures on Tensor Categories and Modular Functors," and I am having some difficulty understanding the definition of $p^\pm$ given on page 49. Throughout much of their exposition, they rely a lot on the ratio of $P^+$ and $P^-$ equalling 1, such as when discussing the equivalence of modular tensor categories and 3D TQFTs, but it isn't entirely clear to me what these terms mean geometrically.

The definition, as stated, is $$ P^\pm = \sum_{i \in \mathcal{I}} \theta_i^{\pm 1} d_i^2 . $$ Here, $\theta_i$ are the twists and $d_i$ are the quantum dimensions, and the sum is over isotopy classes of the tangles.

While it is hard to share geometric intuition over the internet, any attempt would be greatly appreciated!