Gauge theory and Rasmussen's invariant

Details Gauge theory and Rasmussen's invariant Gauge theory and Rasmussen's invariant

2011-10-06

arxiv.org/abs/1110.1297v1

Mathematics

Geometric Topology

21 pages, 3 figures

Scientific paper

We show that Rasmussen's knot-invariant, which provided a lower bound for the slice-genus of knots in the 3-sphere, is equal to an invariant which can be defined in a very similar manner using instanton knot homology. As a corollary, it is shown that Rasmussen's invariant provides a bound for the genus of a bounding surface not only in the standard 4-ball, but in any homotopy 4-ball. Thus, this knot-invariant cannot be used to detect counterexamples to the smooth 4-dimensional Poincar\'e conjecture.

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