Heegaard Floer correction terms and rational genus bounds

Yi Ni Caltech Zhongtao Wu Chinese University of Hong Kong

Geometric Analysis and Geometric Topology mathscidoc:1709.15002

Adv. Math., 267, 360-380, 2014
Given an element in the first homology of a rational homology 3-sphere Y, one can consider the minimal rational genus of all knots in this homology class. This defines a function Θ on H1(Y;Z), which was introduced by Turaev as an analogue of Thurston norm. We will give a lower bound for this function using the correction terms in Heegaard Floer homology. As a corollary, we show that Floer simple knots in L-spaces are genus minimizers in their homology classes, hence answer questions of Turaev and Rasmussen about genus minimizers in lens spaces.
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@inproceedings{yi2014heegaard,
  title={Heegaard Floer correction terms and rational genus bounds},
  author={Yi Ni, and Zhongtao Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927155023690534840},
  booktitle={Adv. Math.},
  volume={267},
  pages={360-380},
  year={2014},
}
Yi Ni, and Zhongtao Wu. Heegaard Floer correction terms and rational genus bounds. 2014. Vol. 267. In Adv. Math.. pp.360-380. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927155023690534840.
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