ETD

• 2-bridge knots
• equivariant concordance
• equivariant sliceness
• eta-polynomial
• strongly invertible knots

This thesis is centered on Sakuma's paper "On strongly invertible knots" (Alg. and TOp. Theories, 1985). In particular, we focus on the computation of eta-polynomial for 2-bridge knots.
After a brief introduction to Knot Theory, we describe in detail strongly invertible knots and 2-bridge knots. We define the equivalence relation of equivariant concordance and show that all 2-bridge knots are strongly invertible.
In 1979, Kojima and Yamasaki defined the eta-polynomial for 2-component links with linking number zero, proving that it is a topological concordance invariant. In 1985, Sakuma adapted this construction to strongly invertible knots and proved that it is an invariant of equivariant concordance. He then stated without proof a formula for the computation of the eta-polynomial in the hyperbolic 2-bridge case.
We present a proof of the formula and supply examples of its standard use, that is as an obstruction to equivariant sliceness. Then we exhibit infinitely many examples of slice and non-slice knots which eta-polynomial vanishes.
We end the thesis with a table of the eta-polynomial of 2-bridge knots up to 9 crossings.