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NONABELIAN MULTIPLICATIVE INTEGRATION ON SURFACES Vital Source e-bog
Amnon Yekutieli
(2015)
World Scientific Publishing
314,00 kr.
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Nonabelian Multiplicative Integration on Surfaces
Amnon Yekutieli
(2015)
Sprog: Engelsk
World Scientific Publishing Co Pte Ltd
1.067,00 kr.
Denne bog er endnu ikke udgivet. Den forventes Dec 2015.
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages): 188 sider
- Udgiver: World Scientific Publishing (Juli 2015)
- ISBN: 9789814663861
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.
Licens varighed:
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Hardback
- Udgiver: World Scientific Publishing Co Pte Ltd (December 2015)
- ISBN: 9789814663847
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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