Abstract
In this paper, we prove a theorem that allows one to evaluate the Heegaard-Floer homology of a link with trivial component added through the Heegaard-Floer homology of the initial link. Bibliography: 8 titles.
Similar content being viewed by others
References
J. A. Baldwin and W. D. Gillam, “Computations of Heegaard-Floer knot homology,” Preprint, arXiv: math.GT/0610167.
P. R. Cromwell, “Embedding knots and links in an open book. I. Basic properties,” Topology Appl., 64,No. 1, 37–58 (1995).
I. Dynnikov, “Arc presentation of links: monotonic simplification,” Fund. Math., 190, 29–67 (2006); arXiv: math.GT/0208153.
C. Manolescu, P. S. Ozsvàth, and S. Sarkar, “A combinatorial description of knot Floer homology,” Preprint, arXiv:math.GT/0607691.
C. Manolescu, P. S. Ozsvàth, Z. Szabò, and D. P. Thurston, “On combinatorial link Floer homology,” Preprint, arXiv:math.GT/0610559.
P. S. Ozvàth and Z. Szabò, “Holomorphic disks and topological invariants for closed 3-manifolds,” Ann. Math. (2), 159,No. 3, 1027–1158 (2004); arXiv:math.SG/0101206.
P. S. Ozvàth and Z. Szabò, “Holomorphic discs and knot invariants,” Adv. Math., 186,No. 1, 58–116 (2004); arXiv:math.GT/0209056.
J. A. Rasmussen, “Floer homology and knot complement,” Ph. D. Thesis, Harvard University (2003); arXiv: math.GT/0306378.
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 37–55.
Rights and permissions
About this article
Cite this article
Karev, M.V. Heegaard-Floer homology of a link with trivial component added. J Math Sci 147, 7145–7154 (2007). https://doi.org/10.1007/s10958-007-0536-0
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10958-007-0536-0