Heegaard Floer correction terms and rational genus bounds

2012/05/31 by Ni, Yi, Wu, Zhongtao
#57M27 #57R58 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1205.7053

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;\mathbb 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.

Related

• Rational genus and Heegaard Floer homology
• Non-simple genus minimizers in lens spaces
• Heegaard diagrams and Floer homology
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