FINAL INFO 
Date & place: Tuesday, May 24th, 810 am in 105
Special office hours: Monday, May 23rd, 8:3010:30am 
Last two topics.
 Notes related to "properly discontinuous group actions"
 Intro to 3manifolds, their Euler characteristic
and gluing 3manifolds from "Topology Now!" by Messer at al
Homework Set 10.
To be handed in Friday, May 13th.  Download as pdf
 Hint to problem 4
 some practice problems
 Escher's Circle Limit III
 An article on The Poincare conjecture and Grigori Perelman from The New York Times, August 22, 2006
 Download as pdf
 Figure 1 and Figure 2
 Summary of what we are/will be discussing: Covering spaces I.  Based on notes taken by Casey Shiring, University of Wisconsin at La Crosse and BSM Fall 2015.
 Here is an animation
showing coverings of a circle.
(The infinite spring of course is homeomorphic to R.)  Download as pdf
 Examples of deformation retracts for practice
 Summary of what we are/will be discussing: Retracts, deformation retracts, homotopy equivalence
Homework Set 9.
To be handed in Friday, May 6th.Homework Set 8.
To be handed in Friday, Apr 29th.Homework Set 7.
To be handed in Friday, Apr 22th.Two nice animations:
In addition: FYI  READING
Homework Set 6.
To be handed in Friday, April 15th.MIDTERM INFO 
Date & place: Tuesday, April 5th, 810 am in 105
Special office hours: Monday, April 4th, 24pm 
Summary of new material from this week, for the midterm:

Homework Set 5.
To be handed in Friday, March 18th.Homework Set 4.
To be handed in Friday, March 11th.Homework Set 3.
To be handed in Friday, March 4th.Week 2.
 from Munkres, discussing the torus case in detail
 from Messer and Straffin, discussing the Mobius case in detail
 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)
 The Klein Bottle (and Mobius strip) (animation)
 If you go to Prague, check out this a Mobius mural
 M.C. Escher's famous Mobius strip
 Homework 1 due Friday, February 19th
 practice problems (no need to hand them in)
 NOTES FOR WEEK1
 Illustration: In topology the cube = the sphere
 R. Messer at al: Topology Now!
 Munkres: Topology
 John Stillwell: Geometry of Surfaces

William Fulton: Algebraic Topology: A First Course
 Alan Hatcher: Algebraic Topology free of charge!
 Jeffrey R. Weeks: The Shape of Space: How to Visualize Surfaces and ThreeDimensional Manifolds

The Shape of the Universe: Ten Possibilities Scientific American article
and more seriously  The class meets Tuesdays and Fridays 8:3010am in Room 105.
 My office hours are: on Feb 11th: 2:304pm. Afterwards, Thursdays, 23:30pm and by appointment
 GRADING: Homework is posted every Friday and is due the next Friday.
 You can get 100 pts on Homework, 100 pts on the Midterm and 100 pts on the Final. That is 300 points altogether. The class is curved with the median placed at around B+.