We show how the von Neumann theory of self-adjoint extensions can be used to investigatequantum systems the configuration space of which can be decomposed into parts of different dimensionalities. The method can be applied in many situations; we illustrate it on examples including point contact spectroscopy, nanotube systems, microwave resonators, or spin conductance oscillations.

Given a 3-holed sphere decomposition of an orientable closed surface, it is shown that each orientation preserving homeomorphism of the surface is isotopic to a composition AB where A is a product of positive Dehn twists and B is a product of negative Dehn twists on the decomposition curves.

We prove that there does not exist any weak coupling limit in the space of superconformal field theories in five and six dimensions, based on an analysis of the representation theory of the corresponding superconformal algebras. Holographically, this implies that superstring theories on AdS6 and AdS7 do not admit tensionless limits. Finally, we discuss the implications of our result on the existence of an action for coincident M5-branes.

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