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portada Nonabelian Multiplicative Integration on Surfaces
Type
Physical Book
Author
Publisher
Language
English
Pages
188
Format
Hardcover
Dimensions
22.9x15.2x1.8 cm
Weight
0.50 kg.
ISBN13
9789814663847
Categories

Nonabelian Multiplicative Integration on Surfaces

Amnon Yekutieli (Author) · World Scientific Publishing Company · Hardcover

Nonabelian Multiplicative Integration on Surfaces - Yekutieli, Amnon

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Synopsis "Nonabelian Multiplicative Integration on Surfaces"

Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult. In our construction, the setup is a Lie crossed module: there is a Lie group H, together with an action on it by another Lie group G. The multiplicative integral is an element of H, and it is the limit of Riemann products. Each Riemann product involves a fractal decomposition of the surface into kites (triangles with strings connecting them to the base point). There is a twisting of the integrand, that comes from a 1-dimensional multiplicative integral along the strings, with values in the group G.The main result of this work is the 3-dimensional nonabelian Stokes theorem. This result is new; only a special case of it was predicted (without proof) in papers in mathematical physics. Our constructions and proofs are of a straightforward nature. There are plenty of illustrations to clarify the geometric constructions.Our volume touches on some of the central issues (e.g., descent for nonabelian gerbes) in an unusually down-to-earth manner, involving analysis, differential geometry, combinatorics and Lie theory -- instead of the 2-categories and 2-functors that other authors prefer.

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