TY - JOUR
T1 - On the Heegaard Floer homology of branched double-covers
AU - Ozsváth, Peter
AU - Szabó, Zoltán
N1 - Funding Information:
∗Corresponding author. School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. E-mail addresses: [email protected] (P. Ozsváth), [email protected] (Z. Szabó). 1Supported by NSF grant number DMS 0234311 and a Sloan Research Fellowship. 2Supported by NSF grant number DMS 0107792 and a Packard Fellowship.
PY - 2005/6/20
Y1 - 2005/6/20
N2 - Let L ⊂ S3 be a link. We study the Heegaard Floer homology of the branched double-cover ∑(L) of S3, branched along L. When L is an alternating link, HF of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose E2 term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of ∑(L).
AB - Let L ⊂ S3 be a link. We study the Heegaard Floer homology of the branched double-cover ∑(L) of S3, branched along L. When L is an alternating link, HF of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose E2 term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of ∑(L).
KW - Alternating links
KW - Branched double-covers
KW - Heegaard Floer homology
KW - Khovanov's homology
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U2 - 10.1016/j.aim.2004.05.008
DO - 10.1016/j.aim.2004.05.008
M3 - Article
AN - SCOPUS:16244407718
SN - 0001-8708
VL - 194
SP - 1
EP - 33
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 1
ER -