Alexanderův polynom

Jančová, Ľubica

Title: Alexander polynomial Author: Ľubica Jančová Department: Department of Algebra Supervisor: doc. RNDr. David Stanovský, Ph.D., Department of Algebra Abstract: The subject of interest of this thesis is the Alexander polynomial in the knot theory as a knot invariant and various methods of its computa- tion. The thesis focuses on the description of the computation of the Alexander polynomial using four different methods, namely: colouring regions of the knot diagram, colouring arcs of the knot diagram, Seifert's method and the method using the Conway polynomial. In the first chapter we introduce basic notions of the knot theory. In the following chapters we describe methods of computa- tion of the Alexander polynomial. The final chapter deals with the possibility of using the Conway polynomial to show that all of the mentioned methods result in the same polynomial. The main result of this thesis are proofs that might lead to the complete proof of equivalence of algorithms of computation of the Alexander polynomial. Keywords: knot theory, Alexander polynomial, knot invariant

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