Munkres page 493 | #3 |

- Let
*M*be an*n*-manifold. Show that*M*is semilocally simply connected, and that*M*has a universal cover which is also an*n*-manifold.

Munkres page 487 | turn in | #1(a) | Friday, April 22 | |

Munkres page 492 | #1 - 3 | turn in | #2(a) | Friday, April 22 |

Munkres page 483 |
#1 - 7 |
turn in |
#3, 4 | Friday, April 15 (these may be turned in on April 22) |

Munkres page 457 | #3, 4 | turn in | #3 | Friday, April 8 |

- Let
*K*be a knot in**R**^{3}, and view*S*^{3}as the 1-point compactification of**R**^{3}(so*K*is in*S*^{3}).

Show that the fundamental groups of**R**^{3}\*K*and*S*^{3}\*K*are isomorphic.

Munkres page 421 | #2, 3 | turn in | #2(a) | Friday, March 18 |

Munkres page 425 | #1, 3 | turn in | #1 | Friday, March 18 |

Munkres page 438 | #2, 3 | turn in | #3 | Friday, March 18 |

- Let
*A*be the union of*n*distinct lines through the origin in**R**^{3}.

Determine the fundamental group of**R**^{3}-*A*. - Let
*G*be the fundamental group of the "double torus"*T*#*T*(see Figure 60.2 on Munkres page 375).

Find a presentation for*G*, and determine the structure of*G*/[*G*,*G*].

Munkres page 359 | #2, 3, 4 | turn in | #2, 4(a) | Friday, March 4 |

Munkres page 375 | #2, 4, 5 | turn in | #2 | Friday, March 4 |

Munkres page 411 | #1 - 6 | turn in | #6 | Friday, March 4 |

Munkres page 366 | turn in | #5, 9 | Friday, February 18 | |

Munkres page 375 | #1, 2 | turn in | #1 | Friday, February 18 |

Munkres page 341 | #1, 3 - 6 | turn in | #1, 3, 4, 6(b) | Friday, February 11 |

Munkres page 347 | turn in | #3, 6, 8 | Friday, February 11 | |

Munkres page 353 | turn in | #2 | Friday, February 11 | |

Munkres page 370 | turn in | #3 | Friday, February 11 | |

Munkres page 330 | #1 - 3 | turn in | #1, 3(a), 3(b) | Thursday, January 27 |

Munkres page 334 | #1 - 5 | turn in | #1(b), 3, 4 | Thursday, January 27 |