Abstract
Braided geometry is a natural generalization of supergeometry and is intimately connected with noncommutative geometry. Synthetic differential geometry is a peppy dissident in the stale regime of orthodox differential geometry, just as Grothendieck's category-theoretic revolution in algebraic geometry was in the middle of the 20th century. Our previous paper [Nishimura (1998) International Journal of Theoretical Physics, 37, 2833–2849] was a gambit of our ambitious plan to approach braided geometry from a synthetic viewpoint and to concoct what is supposedly to be called synthetic braided geometry. As its sequel this paper is intended to give a synthetic treatment of braided connections, in which the second Bianchi identity is established. Considerations are confined to the case that the braided monoidal category at issue is a category of vector spaces graded by a finite Abelian group with its nonsymmetric braiding being given by phase factors. Thus the present paper encompasses physical systems amenable to anyonic statistics.
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Nishimura, H. Synthetic Braided Geometry II. International Journal of Theoretical Physics 40, 1363–1385 (2001). https://doi.org/10.1023/A:1017548326265
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DOI: https://doi.org/10.1023/A:1017548326265