Exploring the Significance of Gauss Words: Why Do Scientists Study Them?

  • Thread starter ArcanaNoir
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In summary, the speaker at a recent seminar on Gauss words mentioned that there are few cases where the Gauss word cannot be reduced to the trivial word. This raises the question of why we even consider Gauss words if they can often be reduced to something simpler. There was some confusion over where to categorize Gauss words, with some suggesting topology and geometry, while others thought algebra might be more appropriate. It turns out there is a topology sub forum, but it must be manually subscribed to in order to see it on the "my pf" homepage.
  • #1
ArcanaNoir
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We had a seminar on Gauss words yesterday, and the speaker brought up the fact that there are relatively few cases where the Gauss word could not be reduced to the trivial word. My question is, if the Gausss words can so often be reduced to the trivial word, how is that a good thing? At the least, how is that not a bad thing? Why do we even consider them?
 
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  • #2
Hey Arcana!

Gauss words... homotopy... differential geometry... (I had to look it up.)
Is this really general math? :wink:
 
  • #3
I didn't know where to put it. Knots are topology. Is that algebra? I wasn't sure. I guess algebra would be more appropriate.
 
  • #4
I'd go for Topology & Geometry.
 
  • #5
Lol I wanted to put it in a topology sub forum but I didn't know we had one! I have all the other math sub forums on my homepage, I must have missed topology somehow. >_<
 
  • #6
lol too. :)

Homepage? What kind of homepage?
 
  • #7
I just meant the "my pf" page.
 
  • #8
I just looked, but there are no links to math sub forums there.
Did you hide them somewhere? ;)
 
  • #9
You have to go to the sub forum, then click forum tools, subscribe to this forum.
 
  • #10
ArcanaNoir said:
You have to go to the sub forum, then click forum tools, subscribe to this forum.

Aha! So you didn't subscribe to the topology sub forum I guess.
I hope you rectified that now. ;P
 
  • #11
Yes I have now happily corrected that oversight.
 

What are Gauss words?

Gauss words are a way of representing knots using a sequence of letters, with each letter corresponding to a crossing in the knot. They were introduced by mathematician Carl Friedrich Gauss in the early 19th century.

What are knot invariants?

Knot invariants are mathematical properties or quantities that do not change when a knot is manipulated or transformed. They are used to classify and distinguish different types of knots.

How are Gauss words related to knot invariants?

Gauss words can be used to calculate knot invariants, such as the Alexander polynomial and the Jones polynomial. These invariants provide important information about the topology and geometry of a knot.

What is the significance of studying Gauss words and knot invariants?

Studying Gauss words and knot invariants is important in the field of topology, as it helps us understand the structure and properties of knots. It also has practical applications in fields such as physics and chemistry.

Are there any limitations to using Gauss words and knot invariants?

While Gauss words and knot invariants are powerful tools for studying knots, they do have some limitations. For example, they may not be able to distinguish between certain types of knots that have the same invariants. Additionally, calculating knot invariants can be a complex and time-consuming process.

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