HW7
From 0506Topology
| # | Week of... | Links (edit) |
|---|---|---|
| Fall | ||
| 1 | Sep 12 | About, Tue, Thu, Std2Disc |
| 2 | Sep 19 | Tue, Thu, HW1, 14 Sets |
| 3 | Sep 26 | Tue, Thu, Photo |
| 4 | Oct 3 | Tue, Thu |
| 5 | Oct 10 | HW2, Tue, Thu |
| 6 | Oct 17 | Tue, Thu, HW3 |
| 7 | Oct 24 | Mon, Tue, Thu |
| 8 | Oct 31 | Tue, Thu, HW4 |
| 9 | Nov 7 | TE1, Tue, Thu |
| 10 | Nov 14 | Tue, Thu, HW5 |
| 11 | Nov 21 | Tue, Thu |
| 12 | Nov 28 | Tue, Thu, HW6 |
| 13 | Dec 5 | Tue, Thu |
| E | Dec 12 | TE2 |
| Spring | ||
| 14 | Jan 9 | Tue, IT83, Thu, HW7 |
| 15 | Jan 16 | Tue, Thu |
| 16 | Jan 23 | Tue, HW8, Thu |
| 17 | Jan 30 | Tue, Thu |
| 18 | Feb 6 | TE3, Tue, Thu |
| 19 | Feb 13 | Tue, Thu |
| R | Feb 20 | |
| 20 | Feb 27 | Tue, Thu, HW9 |
| 21 | Mar 6 | Tue, Thu, HW10 |
| 22 | Mar 13 | Tue, Thu |
| 23 | Mar 20 | Tue, Thu, HW11 |
| 24 | Mar 27 | Tue, Thu |
| 25 | Apr 3 | Tue, Thu, HW12 |
| 26 | Apr 10 | Tue, Thu |
| Study | Apr 17 | Office Hours |
| Exams | Apr 24 | Final, PM |
Homework Assignment 7
required reading. Read, reread and rereread your notes to this point, and make sure that you really, really really, really really really understand everything in them. Do the same every week! Also, read Hatcher's section 1.3.
Just one problem. (due at the end of our class on Thursday, January 26, 2006). Let K be a knot in 
presented by a planar diagram D. With a massive use of Van-Kampen's theorem, show that the fundamental group of the complement of K has a presentation (the "Wirtinger" [1] (http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Wirtinger.html) [2] (http://en.wikipedia.org/wiki/Wirtinger) presentation) with one generator for each edge of D and two relations for each crossing of D, as indicated in the figure below.
Just for fun. Prove that the following two links have homeomorphic fundamental groups (of their complements). In fact, show that their complements are actually homeomorphic. Are the links really the same?
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(See more at [3] (http://www.math.toronto.edu/~drorbn/classes/0405/Topology/HW5/HW.html))
| Above the line, edit only if you are sure | Feel free to edit below the line |
