  We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This
theory can be obtained from 5d MSYM theory by performing the maximal
topological twist. We put the theory on a five-manifold and compute the
partition function. We find that it is a topological quantity, which involves
the Ray-Singer torsion of the five-manifold. For abelian gauge group we
consider the uplift to the 6d theory and find a mismatch between the 5d
partition function and the 6d index, due to the nontrivial dimensional
reduction of a selfdual two-form gauge field on a circle. We also discuss an
application of the 5d theory to generalized knots made of 2d sheets embedded in
5d.
