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The first Alexander Z(Z)–modules of
surface-links and of virtual links
Akio Kawauchi
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Geometry & Topology Monographs 14
(2008) 353–371
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Abstract
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We characterize the first Alexander ℤ[ℤ]–modules of ribbon surface-links in the
4–sphere fixing the number of components and the total genus, and then the first
Alexander ℤ[ℤ]–modules of surface-links in the 4–sphere fixing the number of
components. Using the result of ribbon torus-links, we also characterize the first
Alexander ℤ[ℤ]–modules of virtual links fixing the number of components. For a
general surface-link, an estimate of the total genus is given in terms of the first
Alexander ℤ[ℤ]–module. We show a graded structure on the first Alexander
ℤ[ℤ]–modules of all surface-links and then a graded structure on the first
Alexander ℤ[ℤ]–modules of classical links, surface-links and higher-dimensional
manifold-links.
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Keywords
Alexander module, surface-link, virtual
link, infinite cyclic covering, cokernel-free module,
symmetric module
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Mathematical Subject Classification
Primary: 57M25
Secondary: 57Q35, 57Q45
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Publication
Received: 6 October 2005
Revised: 9 March 2007
Accepted: 9 March 2007
Published: 29 April 2008
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