5 papers
Polynomial knots
Alan Durfee, Donal O'Shea
A polynomial knot is a smooth embedding whose components are polynomials. The case is of particular interest. It is both an object of real algebraic…
Singularities
Alan H. Durfee
This article recounts the interaction of topology and singularity theory (mainly singularities of complex algebraic varieties) which started in the early part of this century and b…
Five Definitions of Critical Point at Infinity
Alan H. Durfee
This survey paper discusses five equivalent ways of defining a ``critical point at infinity'' for a complex polynomial of two variables.
The index of
Alan H. Durfee
Let be a real polynomial of degree with isolated critical points, and let be the index of around a large circle containing the critical points. An element…
Intersection homology Betti numbers
Alan H. Durfee
A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of in…