Amphichiral knots with large 4-genera

Abstract: An oriented knot is called negative amphichiral if it is isotopic to the reverse of its mirror image. Such knots have order at most two in the concordance group, and many modern concordance invariants vanish on them. Nevertheless, we will see that there are negative amphichiral knots with arbitrarily large 4-genera (i.e. which are highly 4-dimensionally complex), using Casson-Gordon signature invariants as a primary tool.

Mathematics

Audience: researchers in the discipline

Caltech geometry/topology seminar