User:Subh83/PlannedContents

The purpose of this page is to assist me not to forget what I thought of doing, even if I were unable to do it due to lack of time. Please feel free to add your comments, suggestions and/or willingness to help with any of the planned items to the talk page of this list.

Planned New Articles
This section lists some articles that I have planned to create in Wikipedia. Please add your comments, suggestions and/or willingness to help with any of the planned items to the talk page.


 * Separate article for Homotopy Equivalence (see Talk:Homotopy).
 * A simple article for describing the differences between homotopy, homology and homeomorphism. (see Talk:Homotopy).
 * Article on local isometric embedding (Janet-Cartan theorem: ref-1, ref-2). Link it to Nash embedding theorem.
 * Article on "gravity induced quantum interference".
 * Article on "Nerve theorem" or "Nerve lemma" (and its sheaf-theoretic generalization).

Planned Contents
This section lists some contents that I have planned to add to some already-existing articles. Please add your comments, suggestions and/or willingness to help with any of the planned items to the talk page.


 * n-sphere: Construction of n-sphere as the quotient space $$D^n / \partial D^n$$.
 * Relative homology: Add better explanation, possibly an illustration. Write explicitly the inclusion, restriction maps on top of the arrows in the chains.
 * Homotopy extension property: Create an illustration for describing HEP.
 * Homotopy extension property: Fix the diagram. It is confusing.
 * Deformation retract: Add an illustrative animation.
 * Universal bundle: Section on on Milnor construction. This is a fundamental construction for defining universal bundles. (ref: Chapter 4 of "Fiber Bundles" by D. Husemoller)
 * Topological K-theory: Expand on the definition.
 * Schr%C3%B6dinger_equation: Axiomatic derivation of the equation using time evolution operator. See the talk page discussion.