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Algebraic Invariants in Knot Theory - NMAG458

Title:	Algebraické invarianty v teorii uzlů
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	winter
E-Credits:	4
Hours per week, examination:	winter s.:2/1, Ex [HT]
Capacity:	unlimited
Min. number of students:	5
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time
Additional information:	https://www2.karlin.mff.cuni.cz/~stanovsk/vyuka/uzly.htm

Guarantor:	doc. RNDr. David Stanovský, Ph.D. doc. RNDr. Jan Šťovíček, Ph.D.
Teacher(s):	Mgr. Radek Olšák doc. RNDr. David Stanovský, Ph.D. doc. RNDr. Jan Šťovíček, Ph.D.
Class:	M Mgr. MSTR M Mgr. MSTR > Povinně volitelné
Classification:	Mathematics > Algebra

Annotation - Czech

Výběrový kurz o využití algebraických a kombinatorických metod k rozpoznávání uzlů.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (10.12.2018)

Literature -

Kunio Murasugi, Knot Theory and Its Applications, Birkhauser 1996

Andrei Sossinsky, Knots, Links and Their Invariants, AMS 2023.

Weiping Li, Lecture Notes on Knot Invariants, World Scientific 2015

Colin Adams, The knot book, Amer. Math. Soc., 2004.

Last update: Stanovský David, doc. RNDr., Ph.D. (22.09.2023)

Requirements to the exam -

Oral exam will test topics covered by the course. For details, see the website.

Last update: Stanovský David, doc. RNDr., Ph.D. (24.02.2021)

Syllabus -

Fundamental concepts of knot theory: equivalence, Reidemeister moves, basic invariants.

Coloring invariants.

Seifert surfaces, Alexander polynomial.

Skein relations, Conway and Jones polynomial.

Braid groups.

Vassiliev invariants.

Last update: Stanovský David, doc. RNDr., Ph.D. (22.09.2023)

Entry requirements -

Basics of general algebra.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (14.05.2020)