Published December 20, 2014
| Submitted
Journal Article
Open
Heegaard Floer correction terms and rational genus bounds
- Creators
- Ni, Yi
- Wu, Zhongtao
Chicago
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Abstract
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.
Additional Information
© 2014 Elsevier Inc. Received 21 September 2012. Accepted 8 September 2014. Available online 26 September 2014. Communicated by Tomasz S. Mrowka. The first author wishes to thank Jacob Rasmussen for asking the question which motivated this work. The first author was partially supported by an AIM Five-Year Fellowship, NSF grant number DMS-1103976 and an Alfred P. Sloan Research Fellowship. The second author was supported by a Simons Postdoctoral Fellowship.Attached Files
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Additional details
- Eprint ID
- 52583
- Resolver ID
- CaltechAUTHORS:20141211-091257551
- AIM Five-Year Fellowship
- NSF
- DMS-1103976
- Alfred P. Sloan Foundation
- Simons Foundation
- Created
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2014-12-11Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field