MikeTateMath.org

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Mike Tate Mathematics

Symbolic Topology Gateway

🧭 Symbolic Topology Gateway

Explore continuity, coverings, deformation, and geometric logic in field-aware topology.

✨ 🕸️ Sheaf Logic
🕸️ Sheaf Logic

Sheaves coordinate data across overlapping patches, forming the core fabric of modern algebraic geometry.

✨ 🌐 Covering Spaces
🌐 Covering Spaces

These maps stretch complex topologies into layered projections, making them navigable and classifiable.

✨ 🌀 Homotopy Fields
🌀 Homotopy Fields

Continuously morph one form into another — preserving identity through fluid shape translation.

✨ 🔄 Ricci Flow
🔄 Ricci Flow

A curvature-flattening transformation — evolving spaces by geometric pressure and smooth topology reshaping.

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🌐 Symbolic Topology Visual Modules

Visually explore homotopy, loop spaces, and cobordism with animated deformation fields and intuitive structures.

🪐 Loop Space Visualizer
🪐 Loop Space Visualizer

The loop space consists of all continuous paths in a space that start and end at the same point. This module shows how families of loops evolve and deform in topological settings.

🧬 Cobordism Fields
🧬 Cobordism Fields

Cobordism studies manifolds as boundaries of higher-dimensional spaces. This animation morphs between 2D shapes to simulate a smooth 3D cobordism process — connecting topology to field theory and category theory.