Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665672 | Advances in Mathematics | 2014 | 21 Pages |
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)
Authors
Yi Ni, Zhongtao Wu,