Teaching‎ > ‎

18.904 Seminar in Topology

Instructor: Yu Pan               Office 2-177              Email: yupan[at]mit.edu              Office hour: By appointment
Writing Instructor: Malcah Effron     Email: meffron[at]mit.edu
Time: MWF 10-11                 Location: 2-151

Textbook: 
    Knots Knotes By Justin Roberts

   Knot Theory and its applications by Kunio Murasugi

   Knots and Links by Dale Rolfsen

Other reference:

Knot Theory by Charles Livingston.

Knots, Links, Braids and 3-Manifolds by V.V. Prasolov and A. B. Sossinsky.

The knot book by Colin Adams.

An Introduction to Knot Theory by Raymond Lickorish.


Please find the course policy here.


Schedule:

 Week Date Topics Sections Presenters
 1 Feb. 6 Introduction to the course  
  Feb. 8 Introduction to Knots theoryRoberts 1 Pan
 2 Feb. 11 Formal definitionsRoberts 2.1-2.2 Varkey, Julian
  Feb. 13 Reidemeister MovesRoberts 2.3 Kaarel, Torri
  Feb. 15 Unknotting numberRoberts 3.2 Earth, Dave
 3 Feb. 19 Linking number Murasugi 4.5 Bau, 
  Feb. 20 3-coloring Roberts 3.3 Leon, Olga
  Feb. 22 p-coloring Roberts 3.4 Dylan, Kevin
 4 Feb. 25 Alexander Polynomial Roberts 3.5 Earth, Bau
  Feb. 27 Problem Seminar  
  Mar. 1 Review of fundamental group Roberts 8.2 Torri, Julian
 5 Mar. 4 Van Kampen's Theorem Roberts 8.3 Varkey, Dave
  Mar. 6 Knot fundamental group Roberts 8.4 Leon, Olga
  Mar. 8 Problem seminar  
 6 Mar. 11 Seifert Surface Roberts 7.1 Kevin, Dylan
  Mar. 13 Genus of knots Roberts 7.2 Kaarel,
  Mar. 15 The Seifert Matrix Murasugi 5.3 
 7 Mar. 18 S-equivalence (I) Murasugi 5.4 
  Mar. 20 S-equivalence (II) Murasugi 5.4 
  Mar. 22 Problem seminar  
 8  Spring Break  
 9 Apr. 1 Alexander Polynomial Murasugi 6.1 
  Apr. 3 Introduction to homology  
  Apr. 5 Cyclic covering Rolfsen 5C 
 10 Apr. 8 Calculation on k-torsion Rolfsen 6B 
  Apr. 10 Problem Seminar  
  Apr. 12 Infinite Covering Rolfsen 7A 
 11 Apr. 15 Holiday  
  Apr. 17 Seifert Surface again Rolfsen 7B 
  Apr. 19 Writing Seminar  
 12 Apr. 22 Problem Seminar  
  Apr. 24 Conway polynomial Murasugi 6.2 
  Apr. 26 Properties Murasugi 6.3 
 13 Apr. 29 Writing Seminar  
  May 1 Signature Murasugi 6.4 
  May 3 Problem Seminar  
 14 May 6 Presentations  
  May 8 Presentations  
  May 10 Presentations  
 15 May 13 Presentations  


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