  We argue that closed string tachyons drive two spacetime topology changing
transitions -- loss of genus in a Riemann surface and separation of a Riemann
surface into two components. The tachyons of interest are localized versions of
Scherk-Schwarz winding string tachyons arising on Riemann surfaces in regions
of moduli space where string-scale tubes develop. Spacetime and world-sheet
renormalization group analyses provide strong evidence that the decay of these
tachyons removes a portion of the spacetime, splitting the tube into two
pieces. We address the fate of the gauge fields and charges lost in the
process, generalize it to situations with weak flux backgrounds, and use this
process to study the type 0 tachyon, providing further evidence that its decay
drives the theory sub-critical. Finally, we discuss the time-dependent dynamics
of this topology-changing transition and find that it can occur more
efficiently than analogous transitions on extended supersymmetric moduli
spaces, which are limited by moduli trapping.
