Higher-order Analogues of the Slice Genus of a Knot

2008/07/02 by Horn, Peter D.
#57M10 #57M25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0807.0434

Abstract

For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann ρ-invariants, which we call higher-order signatures. The higher-order genera offer a refinement of the Grope filtration of the knot concordance group.

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