New lower bounds on the unknotting number of a knot are constructed from the
classical knot signature function. These bounds can be twice as strong as previously
known signature bounds. They can also be stronger than known bounds arising from
Heegaard Floer and Khovanov homology. Results include new bounds on the Gordian
distance between knots and information about four-dimensional knot invariants. By
considering a related nonbalanced signature function, bounds on the unknotting
number of slice knots are constructed; these are related to the property of
double-sliceness.
