Nonabelian Multiplicative Integration on Surfaces by Amnon Yekutieli

By Amnon Yekutieli

Nonabelian multiplicative integration on curves is a classical idea. This quantity is ready the 2-dimensional case, that's even more tricky. In our development, the setup is a Lie crossed module: there's a Lie crew H, including an motion on it via one other Lie team G. The multiplicative necessary is part of H, and it's the restrict of Riemann items. each one Riemann product consists of a fractal decomposition of the outside into kites (triangles with strings connecting them to the bottom point). there's a twisting of the integrand, that comes from a 1-dimensional multiplicative critical alongside the strings, with values within the crew G.

The major results of this paintings is the third-dimensional nonabelian Stokes theorem. This result's new; just a specific case of it was once anticipated (without evidence) in papers in mathematical physics. Our structures and proofs are of an easy nature. there are many illustrations to elucidate the geometric constructions.

Our quantity touches on the various important concerns (e.g., descent for nonabelian gerbes) in an strangely down-to-earth demeanour, regarding research, differential geometry, combinatorics and Lie idea — rather than the 2-categories and 2-functors that different authors prefer.

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