Welcome to MathOverflow

Question

0

Hello, I'm fairly new to graph theory (and math overflow) and I had a question that someone might be able to answer pretty easily on here (please don't assume I know a lot about graph theory just yet). I'm looking at trying to calculate the flux of a chain complex (specifically I'm looking at calculating the flux of a triangle within a graph...I think it's generally called a "3 form" right?) and I was wondering if anyone knew of a place online that had examples of this type of problem with solutions that I could look at? I've read the portion of the wikipedia page on Stokes' Theorem and calculating it with chains, but I'm not sure I fully understand it. Sometimes, a nice example goes a long way. I can calculate the flux when I'm just using 3-D coordinates (from Calculus III), but when the "coordinates" are switched to chains, then I become confused. It doesn't seem like it, but if I'm trying to do something with graph theory that can't be done (like trying to work with two concepts that just don't go together), then please tell me or possibly point me in the right direction. Any and all help/ comments is appreciated!

Ok, let me see if I can convey what I'm essentially trying to get from my question above. Stokes' Theorem provides a way to calculate the flux through a surface. What does it conceptually mean if it is applied to a chain? (could it be interpreted as the rate of "stuff" flowing through the chain?) When it gets down to it, I'm just asking for someone's interpretation of the what the flux means when talking in the context of chains.

edited Jul 8 2010 at 5:20

Yemon Choi
8,456●1●19●45

asked Jul 7 2010 at 21:37

jgbradley1
1●1

5

I think you are likely using the word "graph," and other words, incorrectly. Perhaps if you more precisely stated your question (using words you're absolutely sure you know the meaning of) and gave an example, it would be more understandable? – Daniel Litt Jul 7 2010 at 21:45

The core of this question seems to be a reference request (i.e. "please suggest a place where I can find discussion/explanation of X") rather than a specific mathematical question. Which is fine, but should perhaps be noted by people when they give answers? – Yemon Choi Jul 7 2010 at 22:20

I'm still puzzled by your use of the term "graph" in this context - does this come from notes, or is it your own terminology? – Yemon Choi Jul 8 2010 at 5:19

Also your new question ("please explain this to me") seems to be different from the original one ("where can I find a reference for...?") and less specific. Have you thought about trying one of the sites listed in the FAQ (mathoverflow.net/faq ) as alternative sources of advice? – Yemon Choi Jul 8 2010 at 5:22

1

I suggest you familiarize yourself with the notion of "simplicial complex" and edit the question with the appropriate word substitutions. – S. Carnahan♦ Jul 8 2010 at 13:54

Calculating Flux over a chain complex

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.