Algebraic & Geometric Topology 8 (2008) 885–909

DOI: 10.2140/agt.2008.8.885

Abstract

We obtain new lower bounds for the minimal genus of a locally flat surface representing a 2–dimensional homology class in a topological 4–manifold with boundary, using the von Neumann–Cheeger–Gromov ρ–invariant. As an application our results are employed to investigate the slice genus of knots. We illustrate examples with arbitrary slice genus for which our lower bound is optimal but all previously known bounds vanish.

Keywords

4-manifolds, minimal genus, minimal Betti number, slice genus, L²-signature

Mathematical Subject Classification

Primary: 57M25, 57N13, 57N35, 57R95

References

Publication

Received: 2 August 2007
Revised: 21 April 2008
Accepted: 24 April 2008
Published: 14 June 2008

Authors