|Originally posted by Lagrangian |
Blake, I'm currently writing a paper on pointfree topology (closely related to mereotopology) and Contact Manifolds, which I'm sure you'll find fascinating. It's mostly written under the language of enriched categories and Monoids (which are Petri Nets of sorts). In essence, they should provide us with a greater understanding of Process Calculi, and how an 'automata group' can be studied under a 'complex' (although the term is symplectic, but we're focusing on the complement of symplectic, which is 'contact') manifold. In essence, our findings should pave the way to new insights on solving problems in 4-Manifolds. Such as the isotopy problem and counting pseudo-holomorphic curves, but combinatorially. I have been in correspondence with a couple of professors.
Here's a clue:
Trace monoids are commonly used to model concurrent computation, forming the foundation for process calculi. They are the object of study in trace theory. The utility of trace monoids comes from the fact that they are isomorphic to the monoid of dependency graphs; thus allowing algebraic techniques to be applied to graphs, and vice-versa.
Wanted to respond to this earlier, but honestly, aside from the bits on topology, it was way over my head. I'm a math major by necessity, not by choice . Thankfully a good friend of mine is both a pothead and wrapping up a graduate degree in pure mathematics, so I had him explain your post your post in simplified English. Clearly you're on some next-level shit. It's no wonder you post in this thread, lol.
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