© | Dror Bar-Natan: Classes: 2004-05: Math 1300Y - Topology: | (37) |
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**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 sections 1.1 and 1.2.

**Solve the following problems. ** (But submit only the starred
ones). In Hatcher' book, problems 2, *3, 5, *6, *8, 9, 12, 16ace and
*16bdf in section 1.1 and problems 3, *4, *8, 10, 14 and 22 in section
1.2.

**Just for fun. ** Prove that the following two links have
homeomorphic complements, and in particular, they cannot be told apart
using the fundamental groups of their complements (are the links, in
fact, the same?):

JavaView
applets, left click and drag to rotate, right click for help and
further options.
Mathematica code: s = Sqrt[2]/2; Graphics3D[Join[ First @ TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1], First @ TubePlot[{-2/3 + Cos[t], s Sin[t], s Sin[t]}, {t, 0, 2Pi}, 0.1], First @ TubePlot[{2/3 + Cos[t], s Sin[t], -s Sin[t]}, {t, 0, 2Pi}, 0.1] ]] |

Graphics3D[Join[ First @ TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1], First @ TubePlot[{-4/3 + Cos[t], s Sin[t], s Sin[t]}, {t, 0, 2Pi}, 0.1], First @ TubePlot[{4/3 + Cos[t], s Sin[t], -s Sin[t]}, {t, 0, 2Pi}, 0.1] ]]
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