New examples of dimension zero categories

New Examples of Einstein Metrics in Dimension Four

The holonomy group of a metric g at a point p of a manifold M is the group of all linear transformations in the tangent space of p defined by parallel translation along all possible loops starting at p 1 . It is obvious that a connection can only be the Levi-Civita connection of a metric g if the holonomy group is a subgroup of the generalized orthogonal group corresponding to the signature of ...

Compactifications of Dimension Zero

A New Zero-Dimension Robot Wrist: Design and Accessibility Analysis

This paper presents the design of a robot wrist with zero hand length and unlimited mutually orthogonal joints. This design is an improvement over existing ones. When equipped with this type of wrist, a robot's entire reachable workspace becomes the dexterous workspace. Because some wrist joint limitations may need to be imposed under practical consideration, to better assess this new wrist des...

Triangulated Categories: Definitions, Properties and Examples

Triangulated categories were introduced in the mid 1960’s by J.L. Verdier in his thesis, reprinted in [15]. Axioms similar to Verdier’s were independently also suggested in [2]. Having their origins in algebraic geometry and algebraic topology, triangulated categories have by now become indispensable in many different areas of mathematics. Although the axioms might seem a bit opaque at first si...

Some Examples in Cohomological Dimension Theory

It is well-known that dimX ≤ n if and only if every map of a closed subspace of X into the n-dimensional sphere Sn can be extended over X. It is also well-known that for the cohomological dimension dimGX of X with respect to an abelian coefficient group G, dimGX ≤ n if and only if every map of a closed subspace of X into the Eilenberg-Mac Lane complex K(G,n) extends over X. These properties giv...