Spherical Time

A Mathematical Exploration of Time as Geometry, Topology, and Structure

What if time isn't just a parameter in equations, but a manifold — one with curvature, loops, and algebraic depth?

In Temporal Topology, time is reimagined as a geometric object: capable of folding, looping, compactifying, or even branching like a quantum Riemann surface. Drawing on a rich fusion of differential geometry, algebraic topology, spectral theory, and quantum physics, this book challenges the classical notion of linear time and constructs a new mathematical framework for understanding temporal structures.

Inside, you'll explore:

• Manifolds, fiber bundles, and exotic temporal spaces

• Closed timelike curves and non-orientable chronologies

• Compactified time in quantum field theory and thermodynamics

• Spectral flows, modular symmetries, and fractal time

• Time in complex planes, sheaf theory, and gauge connections

• The topology of causality, time crystals, and chrono-holonomy

Designed for advanced students, physicists, and mathematicians, Temporal Topology offers rigorous definitions, formal theorems, rich illustrations, and speculative insights. Whether you're studying quantum gravity, causality structures, or the foundations of time itself — this book gives you the language, tools, and concepts to ask deeper questions.

Time is not a backdrop. It's a topological protagonist.