Math 692 Spring 2016

Instructor: Robert Lipshitz

Basic course information

Time: MWF 9:00–9:50 a.m.
Place: 104 Deady Hall.
Textbook: None. This seminar is focused on reading journal articles.
Office hours: For now, by appointment.
Final exam: None.


This course is open to mathematics Ph.D. students with an interest in topology. If you are not a mathematics Ph.D. student, you must have my explicit permission to enroll.

Description and goals

Math 692, traditionally called "What Every Topologist Should Know" (WETSK), is a reading seminar in topology. The seminar has three goals:

  • To give students practice reading and understanding mathematics research papers, by reading a variety of well-written and important papers in topology from the last century.
  • To give students practice presenting advanced mathematics, by presenting the papers and getting feedback before and after the presentations.
  • To expose students to some of the central tools, problems and themes in topology over the last century.



In-class presentations 70%
Homework 15%
Class participation 15%


Class format

In a typical meeting, a student will give a 40-minute talk on a pre-chosen research paper. The talk will be followed by five minutes for questions, and five minutes for me to comment further on the paper and its context. Longer papers will span several days, and be presented by several students. Each paper will also have a second reader, who does a cursory reading of the paper and serves as a sounding board for the first reader's presentation.

The first week will be slightly different. The first day is an organizational meeting, where students select readings to present. The next three meetings will be glorified office hours: I will be in the classroom to discuss questions that come up in the readings, and students are encouraged to come to read or discuss the readings with me or each other.

Preparation for presentations

Before giving his/her presentation, each student must do the following, preferably in this order:

  1. Read the paper several times, noting the main results, and outline of the proofs of those results, and any things he/she did not understand when reading. Come up with a tentative outline of the 40-minute talk.
  2. Meet with the paper's second reader to briefly discuss the paper, going through the outcome of (1). (I imagine this meeting will take about half an hour.)
  3. Meet with me to discuss the paper, going through the outcome of (1) as revised following (2). (Again, I imagine this will take about half an hour.) Send me an e-mail about meeting times at least a week before presenting the paper.
  4. Prepare the presentation.
  5. Prepare two homework questions to give the class. These should by questions which:
    • Rely on the material from the talk,
    • Illuminate the content of the paper, and
    • should actually be solvable following the talk.
    Computing examples or filling in the proofs of lemmas often make good homework problems.
  6. Practice the talk once in front of the second reader. This should happen at least two days before giving the talk.
  7. Make revisions to the talk taking into account the second reader's feedback.
  8. Optionally, practice the talk one more time.

Post-presentation feedback

Each presenter will meet with me briefly (roughly 5 minutes) within a few days ofter giving his/her talk to discuss any suggestions I have about presenting the material, and any more mathematical questions that came up.


Each student must solve and turn in solutions to at least four homework problems, of his or her choice, during the quarter.

Students with disabilities

I, and the University of Oregon in general, are committed to an inclusive learning environment. If you have a disability which may impact your performance on exams, please contact the Accessible Education Center to discuss appropriate accommodations. If there are other disability-related barriers to your participation in the course, please either discuss them with me directly or consult with the Accessible Education Center.


Week Date Topic Presenter
1 3/28 Organizational meeting Lipshitz
  3/30 No presentations; class is an opportunity to discuss your reading (optional).  
  4/1 No presentations; class is an opportunity to discuss your reading (optional).  
2 4/4 No presentations; class is an opportunity to discuss your reading (optional).

This is also the last day to drop the class without a W.
  4/5 Steenrod, "Cohomology operations, and obstructions to extending continuous functions" Bradley
  4/8 Steenrod, "Cohomology operations, and obstructions to extending continuous functions" Felix
3 4/11 Fox, "A quick trip through knot theory" Jeff
  4/13 Gordon-Litherland, "On the signature of a link" Keegan
  4/15 Serre, "Homologie singulière des espaces fibrés. Applications" Eric
4 4/18 Serre, "Homologie singulière des espaces fibrés. Applications" Clover
  4/20 Milnor, "On manifolds homeomorphic to the 7-sphere" Bradley
  4/22 Kervaire-Milnor, "Groups of homotopy spheres. I." Leanne
5 4/25 McDuff-Salamon, Introduction to symplectic topology Ben
  4/27 Moser, "On the volume elements on a manifold"
Darboux, "Sur le problème de Pfaff"
  4/29 Hill-Hopkins-Ravanel, "On the non-existence of elements of Kervaire invariant one" Leanne
6 5/2 HOMFLY, "A New Polynomial Invariant of Knots and Links" Jeff
  5/4 Greene, "Alternating links and definite surfaces" Keegan
  5/6 McDuff-Salamon Ben
7 5/9 Gromov, "Pseudoholomorphic curves in symplectic manifolds" Ben
  5/11 Gromov, "Pseudoholomorphic curves in symplectic manifolds" Bradley
  5/13 Gromov, "Pseudoholomorphic curves in symplectic manifolds"

The last day to withdraw from the class is 5/15.
8 5/16 Smith, "Fixed-point theorems for periodic transformations" Eric
  5/18 Borel, "Nouvelle démonstration d’un théeorème de P. A. Smith" Clover
  5/20 May, "A generalization of Smith theory" Eric
9 5/23 Kronheimer-Mrowka, "The genus of embedded surfaces in the projective plane" Demetre
  5/25 Barrat-Milnor, "An example of anomalous singular homology" Clover
  5/27 Chekanov, "Differential algebra of Legendrian links" Keegan
10 5/30 Memorial day holiday  
  6/1 Floer, "Morse theory for Lagrangian intersections" Jeff
  6/3 Floer, "Morse theory for Lagrangian intersections" Ben