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 prove that the group C ∼ $\widetilde{\mathcal {C}}$ of equivariant concordance directed strongly invertible knots, defined by Sakuma (On Algebraic and topological theories (Kinosaki, 1984), Kinokuniya Company Ltd., Tokyo, 1986, pp. 176–196), is not abelian. do so exhibiting an infinite family non-trivial commutators.

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 ...