Twistings, band-sums and L-space surgeries
Twisting operations and band-sum operations enable us to create new knots form given ones.We will discuss if we can obtain L-space knots using these operations. We give a necessary and sufficient condition for a twist family of knots to contain infinitely many L-space knots. We also prove that a non-trivial band sum never yields an L-space knot. This generalizes Krcatovich's result which asserts that a non-trivial connected sum never yields an L-space knot.This is joint work with Ken Baker.