We prove a topological version of abelian duality where the gauge groups are finite abelian. The theories homotopy TFTs, analogues p-form U(1) theories. Using Brown–Comenetz duality, we extend to TFTs $$\pi $$ -finite spectra.

By determining the relation between topological M-theory and Chern-Simons actions for a gauge field constructed from Lie algebra of either SL(2,R)x SL(2,R) or SL(2,C)x SL(2,C), depending on sign space-time curvature, we show that standard exotic 3-dimensional gravity can be recovered M-theory. With this result, provide concrete realisation conjecture by Dijkgraaf et al. stating partition functi...

Starting with topological field theory, we derive space-time uncertainty relation proposed by Yoneya through breakdown of topological symmetry in the large N matrix model. Next, on the basis of only two basic principles, those are, generalized space-time uncertainty principle containing spinor field and topological symmetry, we construct a new matrix model. If we furthermore impose a requiremen...