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# Homework Assignment 5

Assigned Thursday November 25; due Thursday January 6, 3PM, in class

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] ]] ```   (`TubePlot` is from http://www.math.toronto.edu/~drorbn/KAtlas/Manual/TubePlot.html.)