Topological minimal genus and L2–signatures

Cha, Jae Choon

doi:10.2140/agt.2008.8.885

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Topological minimal genus and $L^2$–signatures

Jae Choon Cha

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, $L^2$-signature

Mathematical Subject Classification 2000

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

References

Publication

Received: 2 August 2007

Revised: 21 April 2008

Accepted: 24 April 2008

Published: 14 June 2008

Authors

Jae Choon Cha
Department of Mathematics and Pohang Mathematics Institute Pohang University of Science and Technology Pohang Gyungbuk 790–784 Republic of Korea

Volume 8, issue 2 (2008)