Poincaré Project
I am currently working through the mathematics required to understand the Poincaré Conjecture and the possible solution recently proposed. I want to blog my journey and I started out summarising the basic foundations of pure mathematics necessary to get to the conjecture-specific parts. Now that I've got to explaining the conjecture, posts are about the background in differential geometry to understand the proofs.
Pages in this category
- Journey to the Poincare Conjecture (Aug. 10, 2007 : 1 comment)
- Poincare Project: Thinking Like a Pure Mathematician (Aug. 10, 2007)
- Poincare Project: Adding Structure to Sets (Aug. 10, 2007 : 6 comments)
- Poincare Project: Metric Spaces (Aug. 10, 2007)
- Poincare Project: Open Balls and Continuity (Aug. 10, 2007)
- Poincare Project: Open Sets (Aug. 10, 2007)
- Poincare Project: Topologies and Topological Spaces (Aug. 10, 2007 : 2 comments)
- Poincare Project: Injections, Surjections and Bijections (Feb. 8, 2005)
- Poincare Project: Further Thoughts on Topologies and Open Sets (Feb. 8, 2005)
- Poincare Project: Homeomorphisms (July 1, 2005)
- Poincare Project: Connectedness, Closed Sets and Topological Properties (Feb. 8, 2005 : 1 comment)
- Poincare Project: A Basis for a Topology (Feb. 8, 2005)
- Poincare Project: The Standard Topology for Ordered Sets (Feb. 8, 2005)
- Poincare Project: Open Coverings and Compactness (Aug. 20, 2005)
- Poincare Project: More on Compactness (Aug. 9, 2007)
- Poincare Project: Separation Axioms (Aug. 10, 2007)
- Poincare Project: More on Separation Axioms (Feb. 8, 2005)
- Poincare Project: Manifolds (Feb. 11, 2005)
- Poincare Project: Switching from Analysis to Algebra (March 6, 2005)
- Poincare Project: Binary Operations (March 14, 2005)
- Poincare Project: Associativity (March 14, 2005)
- Poincare Project: Identities and Monoids (Aug. 9, 2007)
- Poincare Project: Inverses (March 19, 2005)
- Poincare Project: Groups (March 26, 2005)
- Poincare Project: Paths (April 21, 2005)
- Poincare Project: Topological Properties Revisited (April 27, 2005 : 1 comment)
- Paths as homeomorphisms of the closed interval from 0 to 1 (June 1, 2005 : 5 comments)
- Homotopy (June 3, 2005)
- Continuous Functions are between Topological Spaces not Sets (Aug. 9, 2007)
- Path Homotopy (July 1, 2005 : 1 comment)
- Homotopy as a Way of Distinguishing Topological Spaces (July 10, 2005 : 4 comments)
- Equivalence Relations (Sept. 28, 2005)
- Equivalence Classes (Aug. 3, 2005)
- Homotopy Classes and Simple Connectedness (Aug. 6, 2005)
- Closed Manifolds (Aug. 9, 2007 : 6 comments)
- The Poincare Conjecture (Aug. 31, 2005 : 2 comments)
- Number of Connected One-Dimensional Manifolds (Oct. 2, 2005 : 11 comments)
- The Circle is Not Simply Connected (Aug. 9, 2007 : 2 comments)
- Poincare Update (Sept. 5, 2006 : 2 comments)
- Coordinate Systems (Aug. 9, 2007)
- Coordinate Systems and Metrics (Nov. 19, 2006)
- Metrics in Two or More Dimensions (Jan. 15, 2007)
- Linear Spaces (Feb. 28, 2007)
- Arrow-type Vectors (Aug. 9, 2007 : 2 comments)
- Linear Spaces: Duck Typing and Tuples (Aug. 9, 2007 : 5 comments)
- Stack-Type Vectors, Part I (Aug. 14, 2007)
- Stack-Type Vectors, Part II (Aug. 23, 2007)
- Stack-Type Vectors, Part III (Dec. 15, 2007)
- Arrows and Stacks as Duals (March 22, 2008)
- One-Forms Form Linear Spaces (March 23, 2008)
- Coordinate Systems and Stack-Type Vectors (March 28, 2008)
- Metrics As Mappings Between Arrows and Stacks (May 4, 2008)
- Metrics Provide An Inner Product (May 11, 2008 : 2 comments)
Created: Aug. 9, 2007
Last Modified: Aug. 9, 2007
Author: jtauber
Last Modified: Aug. 9, 2007
Author: jtauber