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Once a cellular decomposition is chosen, the corresponding space of effective gauge fields is the space of flat connections with singularities on its codimension two skeleton, ${\\cal A}_{C-flat} \\subset \\bar{\\cal A}_M$. If cellular decomposition $C_2$ is finer than cellular decomposition $C_1$, there is a coarse graining map $\\pi_{C_2 \\to C_1}: {\\cal A}_{C_2-flat} \\to {\\cal A}_{C_1-flat}$. 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Zapata","submitted_at":"2005-07-05T05:21:05Z","abstract_excerpt":"A notion of effective gauge fields which does not involve a background metric is introduced. The role of scale is played by cellular decompositions of the base manifold. Once a cellular decomposition is chosen, the corresponding space of effective gauge fields is the space of flat connections with singularities on its codimension two skeleton, ${\\cal A}_{C-flat} \\subset \\bar{\\cal A}_M$. If cellular decomposition $C_2$ is finer than cellular decomposition $C_1$, there is a coarse graining map $\\pi_{C_2 \\to C_1}: {\\cal A}_{C_2-flat} \\to {\\cal A}_{C_1-flat}$. 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