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Abstract: In the context of 2+1-dimensional gravity, we use holonomies of constantconnections which generate a $q$-deformed representation of the fundamentalgroup to derive signed area phases which relate the quantum matrices assignedto homotopic loops.
We use these features to determine a quantum Goldmanbracket commutator for intersecting loops on surfaces, and discuss theresulting quantum geometry.



Author: J.E.Nelson, R.F.Picken

Source: https://arxiv.org/



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