22M:305:001 Topics in Topology

Spring 2010 10:55A - 12:10P TTh N202 LC

Instructor:  Dr. Isabel Darcy                 Office:B1H MLH                     Phone: 335- 0778
Email: idarcy AT math.uiowa.edu
Office Hours: MW 2:30 - 3:20pm, Th 12:30 - 2:30pm, and by appointment.  
Wiki course WWW site:  http://mathwiki.math.uiowa.edu/index.php/Main_Page
Syllabus:  http://www.math.uiowa.edu/~idarcy/COURSES/305/SPRING10/305syl.html

Tentative Schedule  

Week 1 (1/19 - 1/22) Tuesday: Ch 1 pdf (color)
Thursday: Maggie Tomova
Week 2 (1/25 - 1/29) Tuesday: Maggie Tomova: Ch 3
Tuesday Topology Seminar: Maggie Tomova
Thursday: Charlie Frohman
Week 3 (2/1 - 2/5) Tuesday: Ch 2: pdf (color)
3:30 pm Tuesday Topology Seminar: Charlie Frohman
Thursday: Ch 2
Week 4 (2/8 - 2/12) Tuesday: Ch 2, 5 (pre-lecture), post-lecture
Thursday: Ch 4, SB
Week 5 (2/15 - 2/19) Tuesday:
Thursday: SB
Week 6 (2/22 - 2/26) Tuesday: Review, 6C, 6D /(pre-lecture) , post-lecture
Thursday:
Week 7 (3/1 - 3/5) Tuesday: 5.2
Thursday: 5.2, SB
Week 8 (3/8 - 3/12) Tuesday: ch 7, SB
Thursday: 7D_SB
Spring Break Week (3/15 - 3/19)
Week 9 (3/22 - 3/26) Tuesday: Alexanderpolynomialreview
Thursday: Skein relations (SB)
Week 10 (3/29 - 4/2) Tuesday: SB
Thursday: SB
Week 11 (4/5 - 4/9) Tuesday: SB
Thursday: SB
April 10-11 AMS meeting
Week 12 (4/12 - 4/16) Tuesday: SB
Thursday: SB mirrors and ribbons, Visualization of Seifert Surfaces, Julia Collins, Symmetries of rational links, project
Week 13 (4/19 - 4/23) Tuesday: SB Lectures on the topology of 3-manifolds: an introduction to the Casson invariant By Nikolai Saveliev: Lecture 1: Heegaard Splittings
**An introduction to Heegaard Floer homology Peter Ozsath and Zoltan Szabo
An introduction to knot theory By W. B. Raymond Lickorish
What is a Legendrian Knot? Joshua M. Sabloff
Grid Diagrams: [Bru98] H Brunn. Uber verknotete kurven. Verhandlugen des ersten Internationalen Mathematiker- Kongresses, Zurich, pages 256259, 1898.
**Grid diagrams and Legendrian links in lens spaces, Ken Baker, Eli Grigsby (powerpoint) , (pdf)
**Constance Leidy: grid diagram
Ghrist: Intro to homology

Thursday: SB
Week 14 (4/26 - 4/30) Tuesday: Exam 1
Thursday:
Week 15 (5/3 - 5/7) Tuesday:
Thursday:
Final Exam Week (5/17 - 5/21) 9:45 A.M. Tuesday, May 11 2010
Links

Topological Invariants of Knots and Links J. W. Alexander Transactions of the American Mathematical Society, Vol. 30, No. 2 (Apr., 1928), pp. 275-306

A Quick Trip Through Knot Theory by Ralph Fox (1961)