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HEEGAARD FLOER HOMOLOGY AND RATIONAL CUSPIDAL CURVES

Part of: Curves Differential topology Local theory Low-dimensional topology

Published online by Cambridge University Press:  05 December 2014

MACIEJ BORODZIK  and
CHARLES LIVINGSTON
MACIEJ BORODZIK
Affiliation:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland; mcboro@mimuw.edu.pl
CHARLES LIVINGSTON
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA; livingst@indiana.edu

Abstract

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We apply the methods of Heegaard Floer homology to identify topological properties of complex curves in $\mathbb{C}P^{2}$. As one application, we resolve an open conjecture that constrains the Alexander polynomial of the link of the singular point of the curve in the case that there is exactly one singular point, having connected link, and the curve is of genus zero. Generalizations apply in the case of multiple singular points.

MSC classification

Primary: 14H50: Plane and space curves
Secondary: 14B05: Singularities 57M25: Knots and links in $S^3$ 57R58: Floer homology
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e28
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2014

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