## PoincarĂ© Project

I am currently working through the mathematics required to understand the PoincarĂ© Conjecture and the possible solution recently proposed. I want to blog my journey and I'm starting out summarising the basic foundations of pure mathematics necessary to get to the conjecture-specific parts.

- Number of Connected One-Dimensional Manifolds
- The Poincare Conjecture
- Closed Manifolds
- Homotopy Classes and Simple Connectedness
- Equivalence Classes
- Equivalence Relations
- Homotopy as a Way of Distinguishing Topological Spaces
- Path Homotopy
- Continuous Functions are between Topological Spaces not Sets
- Homotopy
- Paths as homeomorphisms of the closed interval from 0 to 1
- Poincare Project: Open Coverings and Compactness
- The Circle is Not Simply Connected

**Categories**: mathematics