WRAPPED M-BRANES AND 3-DIMENSIONAL TOPOLOGIES

The three-dimensional topologies of the membrane of M-theory can be co nstructed by performing Dehn surgery along knot lines. We investigate membranes wrapped around a circle and the corresponding subset of topo logies (Seifert manifolds). The knot lines are interpreted as magnetic flux tubes in an XY model coupled to Maxwell theory. In this model th e eleventh dimension of M-theory gets ''eaten'' by the world-brane met ric. There is argued to be a second-order phase transition at a critic al value of the string coupling constant. The topology fluctuations th at correspond to the knot lines are irrelevant in one phase while they condense in the other phase. (C) 1998 Elsevier Science B.V.