Alladi Ramakrishnan Hall

Quandles: Introduction and the Word Problem

T V H Prathamesh

IMSc

Quandles are algebraic structures equipped with a binary operation
which were introduced to axiomatize knots and Reidemeister moves. Their
applications in knot theory range from providing a invariant of knots(upto
mirror image of a knot), characterizing the colorings of a knot as well as
providing an analogue of Alexander polynomial in terms of an algebraic
structure.

They are also interesting algebraic and combinatorial structures in their
own right and axiomatize some of the properties of conjugation operation of
groups. In this talk, I intend to provide a basic introduction to quandles
and discuss the proof of the undecidability of the word problem of quandles.