Resumen:
By determining the relation between topological M-theory and the Chern-Simons actions for a
gauge field constructed from the Lie algebra of either SL(2, R) × SL(2, R) or SL(2, C) × SL(2, C),
depending on the sign of the space-time curvature, we show that the standard and exotic actions
of 3-dimensional gravity can be recovered from topological M-theory. With this result, we provide
a concrete realisation of a conjecture by Dijkgraaf et al. stating that the partition function of
topological M-theory is equivalent to the partition function of a black hole in a related theory. We
do this for the standard and exotic BTZ black holes in 3-dimensional gravity