Constant connections, quantum holonomies and the Goldman bracket

Abstract

In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate the quantum matrices assigned to homotopic loops. Some features of the resulting quantum geometry are explored, and as a consequence a quantum version of the Goldman bracket is obtained

25 pages, 43 figures, using ATMP style file, to appear Adv.Theor.Math.Phys. Vol 9 (2005)