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Abstract
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We obtain new lower bounds for the minimal genus of a locally flat surface representing a
–dimensional homology class
in a topological –manifold
with boundary, using the von Neumann–Cheeger–Gromov
–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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Keywords
4-manifolds, minimal genus, minimal Betti number, slice
genus, $L^2$-signature
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Mathematical Subject Classification 2000
Primary: 57N13, 57N35, 57R95, 57M25
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Publication
Received: 2 August 2007
Revised: 21 April 2008
Accepted: 24 April 2008
Published: 14 June 2008
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