We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of categories if, and only it non-degenerate. This includes case semisimple modular categories, but also non-semisimple examples such as representations small quantum group at good roots unity. Via cobordism hypothesis, we obtain new 4-dimensional framed topological field theories, which regard versio...

We give a calculation of Picard groups Pic2 of K(2)-local invertible spectra and Pic(L2) of E(2)-local invertible spectra, both at the prime 3. The main contribution of this paper is to calculation the subgroup κ2 of invertible spectra X with (E2)∗X ∼= (E2)∗S as continuous modules over the Morava stabilizer group G2.

Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we establish a semi-invertible multiplicative ergodic theorem that for the first time can be applied to the study of transfer operators associated to the composition ...