Volume 8, issue 2 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Topological minimal genus and $L^2$–signatures

Jae Choon Cha

Algebraic & Geometric Topology 8 (2008) 885–909
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