Groups of Flagged Homotopies and Higher Gauge Theory

Details Groups of Flagged Homotopies and Higher Gauge Theory Groups of Flagged Homotopies and Higher Gauge Theory

1999-04-06

arxiv.org/abs/math/9904026v3

Mathematics

Geometric Topology

11 pages, LaTeX

Scientific paper

Groups $\Pi_k(X;\sigma)$ of "flagged homotopies" are introduced of which the usual (abelian for $k>1$) homotopy groups $\pi_k(X;p)$ is the limit case for flags $\sigma$ 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 $\Pi_k$ in $G=exp A$.

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