Article ID Journal Published Year Pages File Type
4665672 Advances in Mathematics 2014 21 Pages PDF
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)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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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