homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
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For a connected finite planar graph the numbers of edges, vertices and number of regions enclosed by edges (“faces”) always satisfies the relation
By passing to the one-point compactification of the plane, which is the 2-sphere, we may think of the planar graph as a polyhedron embedded in the 2-sphere. Under this identification the above is a special case of the general formula for Euler characteristic of CW-complexes. See at Euler characteristic – Of topological spaces.
That the loop order of a (planar) Feynman diagram is its contribution in powers of Planck's constant to the scattering amplitude is a consequence of Euler’s formula. See at loop order – Relation to powers in Planck’s constant
Last revised on August 1, 2018 at 17:36:57. See the history of this page for a list of all contributions to it.