Instantons, concordance, and Whitehead doubling

Whitehead Doubling Persists

Even though the (untwisted) Whitehead doubling operation kills all known abelian invariants of knots (and makes them topologically slice), we show that it does not kill the rational function that equals to the 2-loop part of the Kontsevich integral.

Whitehead method and Geneti Algorithms

Kervaire invariant and Whitehead square

In this note, we try to shed some light on the relationships between the Hopf invariant, Kervaire invariant, and Whitehead square. More specifically, we prove two classical results (theorems 2.1 and 3.1) in a way that seems more transparent (at least to the author) than what is found in the literature. No new results are claimed, only a different exposition. In addition to the references cited,...

Whitehead method and Genetic Algorithms

In this paper we discuss a genetic version (GWA) of the Whitehead’s algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead’s algorithm in free groups of rank ≥ 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of the Whitehead’s Problem ...

Alfred North Whitehead

Alfred North Whitehead (1861-1947) never wrote a comprehensive work in philosophy of education, but he occasionally delivered lectures concerned with educational policy. These incisive talks are collected in his book The Aims of Education and Other Essays. Whitehead and Dewey were contemporaries, and their ideas are in some notable respects similar. Like Dewey, Whitehead stresses the importance...