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2008 Topological minimal genus and $L^2$–signatures
Jae Choon Cha
Algebr. Geom. Topol. 8(2): 885-909 (2008). 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.

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Jae Choon Cha. "Topological minimal genus and $L^2$–signatures." Algebr. Geom. Topol. 8 (2) 885 - 909, 2008. https://doi.org/10.2140/agt.2008.8.885

Information

Received: 2 August 2007; Revised: 21 April 2008; Accepted: 24 April 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1162.57016
MathSciNet: MR2443100
Digital Object Identifier: 10.2140/agt.2008.8.885

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

Rights: Copyright © 2008 Mathematical Sciences Publishers

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