User:J D Bowen

Hi there! I'm a senior mathematics major at the University of San Francisco, currently applying to PhD programs around the US and Canada.

I'm particuarly interested in topology, and it is in this area I intend to contribute to Proofwiki.

= Pages =

I have written or extensively contributed to many completed and nearly completed pages, including, but not limited to:


 * Metrics Induce a Topology
 * Ostrowski's Theorem
 * Lebesgue Integral is Extension of Riemann Integral
 * Fundamental Theorem of Finite Abelian Groups
 * Existence of Non-Measurable Sets
 * Sum of Reciprocals is Divergent
 * Homotopy Groups are Groups
 * Brouwer's Fixed Point Theorem
 * Fundamental Theorem of Algebra
 * Weak Whitney Immersion Theorem
 * Classification of Compact One-Manifolds
 * Classification of Compact Two-Manifolds

= Projects =

I'm working on putting all of my lecture notes in topology up here, drawing heavily on 3 reference texts: Guillemin and Pollacks Differential Topology, Bredon's Topology and Geometry , and Hocking and Youngs Topology.

Articles I've written which need LOTS of additional work:


 * Poincare Conjecture (lols)
 * H-Cobordism Theorem (ditto)
 * Fundamental Theorem of Finite Abelian Groups completed
 * Kuratowski’s Theorem
 * Everything relating to homotopy groups
 * The series of articles on degree and intersection theory

Articles which only need a little more:


 * Classification of Compact One-Manifolds
 * Classification of Compact Two-Manifolds

Articles I'd like to begin soon:


 * Alexander Polynomial is a Knot Invariant
 * HOMFLY Polynomial is a Knot Invariant
 * Classification of Compact Three-Manifolds Supporting Zero-Curvature Geometry (this one's a ways away)