Mathematics – Geometric Topology
Scientific paper
2006-09-14
Mathematics
Geometric Topology
17 pages; revised a few statements
Scientific paper
We obtain new lower bounds of 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 $\rho$-invariant. As an application our results are employed to investigate the slice genus of knots. We illustrate examples with arbitrarily large slice genus for which our lower bound is optimal but all previously known invariants vanish.
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