MWinter4

I plan to write and update articles on geometry, polytope theory, graph theory, rigidity theory and topology. You can see my projects in the subpages

Some projects

Whitney trick

The Whitney trick is mentioned in several articles, and details on it are distributed across these. This includes the articles.

• Whitney embedding theorem
• Whitney disc
• Casson handle
• 4-manifold

I am writing a dedicated article User:MWinter4/Whitney trick to focus this information.

Graph embeddings

A graph embedding is, as the name suggests, an embedding of a graph, with no specifics for where the graph is embedded into. However, the current article Graph embedding addresses embeddings into surfaces only. Also other article titels sound as if they are more general, but are eventually intrinsically planar, such as:

• Topological graph
• Geometric graph

I am currently writing a more general article User:MWinter4/Graph embedding. Its content should already now make clear that the concept is much broader.

YΔ- and ΔY-transformations

YΔ- and ΔY-transformations are a pair of operations on graphs. Their main application outside of mathematics is in electrical engineering. The article Y-Δ transform is about this application. It is rather technical and does not give a suitable mathematical overview.

I wrote the article YΔ- and ΔY-transformation to discuss these operations from a mathematical perspective.

Many mathematical Wikipedia articles still link to the electrical engineering article. There are also many articles that introduce these transformations on their own:

• Linkless embedding (also defines YΔY-reducible graphs)
• Petersen family
• Steinitz's theorem

There currently exists a sligth inconsistency in terminology, which is already visible from the article titles. We have

• Y-Δ transform
• YΔ-transformation

I prefer the latter. It is more consistent with YΔY-reducible graphs. I am aware that most article (also the mathematical ones) currently use the former.

Fundamentals of rigidity theory

The fundamentals of rigidity theory are currently spread over several articles, most notably

• Structural rigidity
• Geometric rigidity

I am writing User:MWinter4/Framework (rigidity theory) to introduce frameworks and their rigidity theory specifically. This will repeat a lot of the content in the article Geometric rigidity which I believe should then be rewritten to be more general.

Likewise, the mathematical theory of the Maxwell-Cremone correspondence is spread over several articles:

• Steinitz theorem
• Tutte embedding
• Cremona diagram

I am working to centralize this into the article User:MWinter4/Maxwell-Cremona correspondence.

Authored articles in mainspace

• Heawood family

• Kotzig's conjecture

• YΔ- and ΔY-transformations