M 392C (57675) Knot Theory
This course will be an introduction to knot theory. Topics covered will include: the Seifert form; the infinite cyclic covering; the Alexander-Conway polynomial; the Blanchfield form; the Tristram-Levine signatures; the Goeritz form; alternating knots; the Kauffman bracket and the Jones polynomial; skein equivalence; knot concordance; higher-dimensional knots.
Prerequisites:
A knowledge of basic algebraic topology (fundamental group, covering spaces, homology) as covered in the Algebraic Topology prelim course.
Textbook(s):
None is required, but the following books may be useful:
G. Burde and H. Zieschang, "Knots", de Gruyter, 1985.
P. Cromwell, "Knots and Links", Cambridge University Press, 2004.
W.B.R. Lickorish, "An Introduction to Knot Theory", Graduate Texts in
Mathematics 175, Springer, 1997.
Time: TTH 9:30 – 11:00 am
Room: RLM 9.166
Instructor: Cameron Gordon
Course Description:
This course will be an introduction to knot theory. Topics covered will include: the Seifert form; the infinite cyclic covering; the Alexander-Conway polynomial; the Blanchfield form; the Tristram-Levine signatures; the Goeritz form; alternating knots; the Kauffman bracket and the Jones polynomial; skein equivalence; knot concordance; higher-dimensional knots.
Prerequisites:
A knowledge of basic algebraic topology (fundamental group, covering spaces, homology) as covered in the Algebraic Topology prelim course.
Textbook(s):
None is required, but the following books may be useful:
G. Burde and H. Zieschang, "Knots", de Gruyter, 1985.
P. Cromwell, "Knots and Links", Cambridge University Press, 2004.
W.B.R. Lickorish, "An Introduction to Knot Theory", Graduate Texts in
Mathematics 175, Springer, 1997.