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#New_article_for_homotopy_equivalence).
• A simple article for describing the differences between homotopy, homology and homeomorphism. (see Talk:Homotopy#Homology.2C_homotopy_and_homeomorphism).
• 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.
• Schrödinger_equation: Axiomatic derivation of the equation using time evolution operator. See the talk page discussion.