Introduction to Topology
  Spring 2014
  
Last modified on: Friday, 25-Apr-2014 09:33:40 CEST
            

Homework Set 8.

To be handed in Thuesday, April 29th.
  • Download as pdf

    "HANDOUTS"

    The notation in these summaries is a little different than that we use in class.
  • Homotopy of paths (From Hatcher's Notes (see "literature used" below))
  • The fundamental group (From Topology Now (see "literature used" below))
  • Free groups and generators (From a combinatorial topology book by Stillwell)
  • Animation: the fundamental group of the torus is abelian(for the meridian "alpha" and longitudinal "beta" loops we have that alpha*beta is homotopic to bet*alpha)

  •   Midterm: April 1st, 8-10 am in 105
      NO CLASS April 3rd, however, we will have a double-class, March 27th, 8:30-10 am instead  
     
  • Midterm info
  • Triangulation of surfaces
  • Summary — the Euler number (the summary is from here)  
     
  • Homework Set 7.

    To be handed in Thursday, March 27th.
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  • Homework Set 6.

    To be handed in Thursday, March 20th.
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  • Proof of the Heine-Borel theorem - missing part.
  • Commutative diagrams
  • A Peano-curve. Namely, the Hilbert-curve. (An example of a "space filling curve".
  • Space filling curve art and art generator
  • Homework Set 5.

    To be handed in Thursday, March 13th.
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  • The Universe as a doughnut
  • Homework Set 4.

    To be handed in Thursday, March 6th.
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  • Homework Set 3.

    To be handed in Thursday, February 27th.
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  • Animation: The Klein Bottle (and Mobius strip)
  • If you go to Prague, check out this a Mobius mural.
  • Finally, here is a summary of what we did week 2-3 new topologies from old: subspace, quotient topologies, cut-and-paste arguments
  • Homework Set 2.

    To be handed in Thursday, February 20th.
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  • Exercises 2. (for practice, no need to hand these in)
  • Week 1. summary

  • Practice problems and summary of what we did so far
  • Illustration: Stereographic projection - animation
  • Stereographic projection from a a complex analysis textbook (since they place the unit sphere differently in the coordinate system as we did in class, the formulae are different a bit)
  • Homework Set 1.

    To be handed in Thursday, February 13th.
  • Download as pdf
  • Exercises 1. (for practice, no need to hand these in)
  • Illustration: In topology the cube = the sphere
  • Literature

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