Minimal Index and Dimension for 2-C*-Categories with Finite-Dimensional Centers

Minimal Hypersurfaces with Finite Index

In an article of Cao-Shen-Zhu [C-S-Z], they proved that a complete, immersed, stable minimal hypersurface M of R with n ≥ 3 must have only one end. When n = 2, it was proved independently by do Carmo-Peng [dC-P] and FischerColbrie-Schoen [FC-S] that a complete, immersed, oriented stable minimal surface in R must be a plane. Later Gulliver [G] and Fischer-Colbrie [FC] proved that if a complete, ...

Higher-dimensional categories with finite derivation type

We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions f...

2-C∗-Categories with non-simple units

Minimal Bratteli Diagrams and Dimension Groups of Af C-algebras

A method is described which identifies a wide variety of AF algebra dimension groups with groups of continuous functions. Since the continuous functions in these groups have domains which correspond to the set of all infinite paths in what will be called minimal Bratteli diagrams, it becomes possible, in some cases, to analyze the dimension group’s order preserving automorphisms by utilizing th...

Residually Finite Dimensional C*-algebras

A C*-algebra is called residually finite dimensional (RFD for brevity) if it has a separating family of finite dimensional representations. A C*-algebra A is said to be AF embeddable if there is an AF algebra B and a ∗-monomorphisms α : A→ B. In this note we discuss the question of AF embeddability of RFD algebras. Since a C*-subalgebra of a nuclear C*-algebra must be exact [Ki], the nonexact R...