# (2+1)-dimensional topological gravity

Physicists became interested in the relation between Chern–Simons theory and gravity during the 1980s.[1] During this period, Edward Witten[2] argued that 2+1D topological gravity is equivalent to a Chern–Simons theory with the gauge group ${\displaystyle SO(2,2)}$ for a negative cosmological constant, and ${\displaystyle SO(3,1)}$ for a positive one. This theory can be exactly solved, making it a toy model for quantum gravity. The Killing form involves the Hodge dual.