Miscellaneous

Non-Trivial Topology of SO(3): Seeing the loop that cannot be shrunk to a point (Penrose’s The Road to Reality)

Understanding Contact Structure Through Legendrian Curves: A Comparison Between Thurston’s Approach and Arnold’s Approach

Exploring the Lorentzian Space: Sphere of Radius √-1

Differentiation of Vector Fields on Manifolds (Arnold’s Math. Methods & Penrose’s The Road to Reality)

Time-Orientability of Lorentzian Metrics on the Mobius Band

Connected Components of a Quadric in RP(3)

Riemann Surfaces: Construction via Group Action

Riemann Surfaces: Multiplicity of a Map at a Point (19/09/2025)

Examples of Riemann Surfaces: Part 1 (Updated: 21/09/2025)

Lorentzian Vector Spaces and Lorentzian Manifolds