Hyperbolic Geometry For Non-Differential Topologists

Hyperbolic Geometry

Hyperbolic geometry for colour metrics.

It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., co...

Interpreter for topologists

Let M be a transitive model of set theory. There is a canonical interpretation functor between the category of regular Hausdorff, continuous open images of Čech-complete spaces of M and the same category in V , preserving many concepts of topology, functional analysis, and dynamics. The functor can be further canonically extended to the category of Borel subspaces. This greatly simplifies and e...

Analytic Novikov for topologists

We explain for topologists the “dictionary” for understanding the analytic proofs of the Novikov conjecture, and how they relate to the surgery-theoretic proofs. In particular, we try to explain the following points: (1) Why do the analytic proofs of the Novikov conjecture require the introduction of C-algebras? (2) Why do the analytic proofs of the Novikov conjecture all use Ktheory instead of...

Numerical studies of non-local hyperbolic partial differential equations using collocation methods

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...