In recent years, it has been discovered that invariants of three dimensional topological objects, such as links and three dimensional manifolds, can be constructed from various tools of mathematicalâ€¦ (More)

Using the theory of measurable categories developped in [Yet03], we provide a notion of representations of 2-groups more well-suited to physically and geometrically interesting examples than thatâ€¦ (More)

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural " tangentâ€¦ (More)

We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing Topologicalâ€¦ (More)

Teichmiiller theory for super Riemann surfaces is rigorously developed using the supermanifold theory" of Rogers. In the case of trivial topology in the soul directions, relevant for superstringâ€¦ (More)

Several series of 2-aryl or heterocyclic-imidazoline compounds have been prepared and evaluated in vitro as imidazoline sites (I1 and I2) and alpha-adrenergic (alpha1 and alpha2) receptor ligands.â€¦ (More)

We consider two related approaches to quantizing general relativity which involve replacing point set topology with category theory as the foundation for the theory. The ideas of categorical topologyâ€¦ (More)

We propose a new line of attack to create a finite quantum theory which includes general relativity and (possibly) the standard model in its low energy limit. The theory would emerge naturally fromâ€¦ (More)