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Heegaard Floer correction terms and rational genus bounds

Ni, Yi and Wu, Zhongtao (2014) Heegaard Floer correction terms and rational genus bounds. Advances in Mathematics, 267 . pp. 360-380. ISSN 0001-8708. doi:10.1016/j.aim.2014.09.006. https://resolver.caltech.edu/CaltechAUTHORS:20141211-091257551

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.aim.2014.09.006DOIArticle
http://www.sciencedirect.com/science/article/pii/S0001870814003077PublisherArticle
http://arxiv.org/abs/1205.7053arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
AIM Five-Year FellowshipUNSPECIFIED
NSFDMS-1103976
Alfred P. Sloan FoundationUNSPECIFIED
Simons FoundationUNSPECIFIED
Subject Keywords:Heegaard Floer homology; Correction terms; Rational genus; Lens space; Simple knots
DOI:10.1016/j.aim.2014.09.006
Record Number:CaltechAUTHORS:20141211-091257551
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141211-091257551
Official Citation:Yi Ni, Zhongtao Wu, Heegaard Floer correction terms and rational genus bounds, Advances in Mathematics, Volume 267, 20 December 2014, Pages 360-380, ISSN 0001-8708, http://dx.doi.org/10.1016/j.aim.2014.09.006. (http://www.sciencedirect.com/science/article/pii/S0001870814003077)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52583
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:11 Dec 2014 21:33
Last Modified:10 Nov 2021 19:42

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