#### 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.

Done