  We propose that a class of new topologies, for which there is no classical
solution, should be included in the path integral of three-dimensional pure
gravity, and that their inclusion solves pathological negativities in the
spectrum, replacing them with a nonperturbative shift of the BTZ extremality
bound. We argue that a two-dimensional calculation using a dimensionally
reduced theory captures the leading effects in the near extremal limit. To make
this argument, we study a closely related two-dimensional theory of
Jackiw-Teitelboim gravity with dynamical defects. We show that this theory is
equivalent to a matrix integral.
