[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vp / vr / w / wg / wsg / wsr / x / y ] [Search | Home]
I made a new field of mathematics
Images are sometimes not shown due to bandwidth/network limitations. Refreshing the page usually helps.

You are currently reading a thread in /sci/ - Science & Math

File: fat graph theory.png (119 KB, 1536x1352) Image search: [iqdb] [SauceNao] [Google]
119 KB, 1536x1352

I call it pipe theory, or fat-graph theory. Its 1 dimension up from normal, 'thin' graph theory. As seen in 1a, the vertices become 2D smooth, non intersecting curves, and the edges become surfaces with boundaries only on the curves in 1b. All the fat graphs drew here are 'volumetric' graphs, the equivalent of planar thin graphs. meaning the surfaces do not intersect each other. The process of 'fattening up' a planar graph to a volumetric is however not just redrawing all the lines as surfaces, as seen in 3, fattening up a thin graph requires a different configuration than the thin graph to make the graph representation volumetric.

I have shown in 4 that any planar thin graph can be fattened up by rotating the graph around a vector not intersecting the graph.

I have a conjecture that i have not been able to prove. First lets define some termsWhen you thin down a fat graph, you get the corresponding thin graph A volumetric fat graph is 'genetically fat' if they can not be thinned down. My conjecture is that no genetically fat graphs exists.

Another conjecture is that the number of volumes separated by surfaces in a fat graph is equal to the number of areas separated by edges in the thinned down graph (given by Eulers formula)

The stronger form of the conjectures is that all of fat-graph theory is equivalent to graph theory on the thinned down graphs, in other words, this new fields yields nothing new to mathematics.

Anyone wiling to help me prove this?
>>
>amerimath
>>
Neato. I'll look at this later.
>>
Formalize it and come back.
You didn't even bother drawing the pics in a way that shows what's in the fore-and background.

The chance that the questions are not questions of homotopy and homology theory is practically zero.
>>
>>7767891
Already used by algebraic topologists forever ago
>>
>>7767891
>pipe theory
>>
>>7768036
Kek'd
>>
>no genetically fat graphs exists

Check you fucking privileges, some people just can't lose weigtht get over it.
>>
Instead of inventing new "notation" try looking at a problem or invent a problem and use your new notation to solve it.
>>
>>7767891
If all fat graphs are 2D cylindrical surfaces connected by 1-Spheres, I would think it wouldn't be too hard to construct a deformation retraction onto some 1D graph.

To be honest none of what you have done seems even remotely rigorous. You even claimed that you showed that any planar graph can be "fattened up" when all you did is draw a picture. For anyone to be able to construct a real proof, you need to come up with precise definitions for these constructions.
>>
>>7767891
>yfw I publish first
>>
Isn't this just n-category theory?
>>
>>7767891
You can probably get the same things with graph theory if you just draw your lines between nodes funny and curved. Don't think you've got something new here, but I'm not a mathemagician so wtf do I know
>>
>>7768159
Well I'm not going to spend a lot of time formalizing it when it already exists.

Ill take a look at the things mentioned itt.