geodesics Archives - Quantum Calculus

Simple Closed Geodesics

By oliverknill April 13, 2025 April 13, 2025

Given a q-manifold, we have a geodesic dynamics T:P -> P, where P is the oriented frame bundle. Most geodesics are not simple but we can look for the number of simple closed geodesics and so investigate questions close to the Ljusternik-Schnirelmann theme in the classical setup. For any 2 …

geodesics, simplicial complex

Shashibo Geodesics

By oliverknill January 12, 2025 January 13, 2025

The Shashibo puzzle is a game in the category of geometrically realized simplicial complexes of dimension q=3. One can also play it combinatorially, meaning to disregard geometric realization and just look at finite set of finite sets. One can see it as a playing with 3-dimensional complexes generated by twelve …