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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 2023
Semester:	winter
E-Credits:	4
Hours per week, examination:	winter s.:2/1, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://www2.karlin.mff.cuni.cz/~stanovsk/vyuka/uzly.htm

Guarantor:	doc. RNDr. David Stanovský, Ph.D.
Class:	M Mgr. MSTR M Mgr. MSTR > Povinně volitelné
Classification:	Mathematics > Algebra

Annotation - Czech

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

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

Literature -

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

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.

Requirements to the exam -

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

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

Syllabus -

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

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.

Entry requirements -

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

Basics of general algebra.