Groups of Flagged Homotopies and Higher Gauge Theory

Author： Dolotin V.  

Publisher： Springer Publishing Company

ISSN： 1079-2724

Source： Journal of Dynamical and Control Systems, Vol.05, Iss.4, 1999-10, pp. : 547-563

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Abstract

Groups Πk(X;) of “flagged homotopies” are introduced of which the usual (abelian for k > 1) homotopy groups k(X;p) is the limit case for flags  contracted to a point p. The calculus of exterior forms with values in an algebra A is developped of which the limit cases are the differential forms calculus (for A = {\Bbb R}) and gauge theory (for 1-forms). Moduli space of integrable forms with respect to higher gauge transforms (cohomology with coefficients in A) is introduced with elements giving representations of Πk in G = expA.

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