Heegaard Floer correction terms and rational genus bounds |
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Authors: | Yi Ni Zhongtao Wu |
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Institution: | Department of Mathematics, Caltech, MC 253-37, 1200 E California Blvd, Pasadena, CA 91125, United States |
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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. |
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Keywords: | Heegaard Floer homology Correction terms Rational genus Lens space Simple knots |
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