Groups of Flagged Homotopies and Higher Gauge Theory

1999/04/06 by Valery V. Dolotin, Dolotin, Valery V.
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #hep-th #math.AT #math.GT

paper · pdf · doi:10.48550/arxiv.math/9904026

11 pages, LaTeX

arxiv created 2001/02/15 · arxiv updated 2009/11/30

Abstract

Groups Π_k(X;σ) of "flagged homotopies" are introduced of which the usual (abelian for k>1) homotopy groups π_k(X;p) is the limit case for flags σ contracted to a point p. Calculus of exterior forms with values in algebra A is developped of which the limit cases are differential forms calculus (for A=\bb 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 Π_k in G=exp A.

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