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as usual I need help with some definitions regarding many-loop calculations.

In particular what do we mean with planar and non-planar topologies exactly?

I have an idea but I'm really not sure how to formalize it for an arbitrary big number of loops and legs.

Second, once the definition is taken, which different difficulties have to be overcome in the evaluations of the planar and non-planar topologies? I ask this simply because I notice that usually the big calculations are done dividing the two contributions and analyzing them in different steps. Why is it so?

Thank you very much

Sleuth