  We study topology change in (2+1)D gravity coupling with non-Abelian SO(2,1)
Higgs field from the point of view of Morse theory. It is shown that the Higgs
potential can be identified as a Morse function. The critical points of the
latter (i.e. loci of change of the spacetime topology) coincide with zeros of
the Higgs field. In these critical points two-dimensional metric becomes
degenerate, but the curvature remains bounded.
