Topological minimal genus and L2–signatures

Cha, Jae Choon¹

¹Department of Mathematics and Pohang Mathematics Institute, Pohang University of Science and Technology, Pohang Gyungbuk 790–784, Republic of Korea

Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 885-909

Résumé

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.

Détail

DOI : 10.2140/agt.2008.8.885

Keywords: 4-manifolds, minimal genus, minimal Betti number, slice genus, $L^2$-signature

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