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Signatures of colored links with application to real algebraic curves


Florens, V (2005). Signatures of colored links with application to real algebraic curves. Journal of Knot Theory and Its Ramifications, 14(7):883-918.

Abstract

We construct the signature of a μ-colored oriented link, as a locally constant integer valued function with domain (S1 - {1})μ. It restricts to the Tristram–Levine's signature on the diagonal and the discontinuities can occur only at the zeros of the colored Alexander polynomial. Moreover, the signature and the related nullity verify the Murasugi–Tristram inequality. This gives a new necessary condition for a link to bound a smoothly and properly embedded surface in B4, with given Betti numbers. As an application, we achieve the classification of the complex orientations of maximal plane non-singular projective algebraic curves of degree 7, up to isotopy.

We construct the signature of a μ-colored oriented link, as a locally constant integer valued function with domain (S1 - {1})μ. It restricts to the Tristram–Levine's signature on the diagonal and the discontinuities can occur only at the zeros of the colored Alexander polynomial. Moreover, the signature and the related nullity verify the Murasugi–Tristram inequality. This gives a new necessary condition for a link to bound a smoothly and properly embedded surface in B4, with given Betti numbers. As an application, we achieve the classification of the complex orientations of maximal plane non-singular projective algebraic curves of degree 7, up to isotopy.

Citations

6 citations in Web of Science®
5 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Link signatures; Casson–Gordan invariants; slice genus; real algebraic curves
Language:English
Date:2005
Deposited On:19 Feb 2010 16:02
Last Modified:05 Apr 2016 13:24
Publisher:World Scientific Publishing
ISSN:0218-2165
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1142/S0218216505004093
Related URLs:http://riemann.unizar.es/geotop/pub/vincent/signalg.pdf

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