2018/10/23 by Eugene Gorsky, Beibei Liu, Gorsky, Eugene +3
Mathematics · Medicine · #Geometric and Algebraic Topology #Botulinum Toxin and Related Neurological Disorders
paper · pdf · doi:10.48550/arxiv.1810.10178
We study Heegaard Floer homology and various related invariants (such as the\nh-function) for two-component L-space links with linking number zero. For\nsuch links, we explicitly describe the relationship between the h-function,\nthe Sato-Levine invariant and the Casson invariant. We give a formula for the\nHeegaard Floer d-invariants of integral surgeries on two-component L-space\nlinks of linking number zero in terms of the h-function, generalizing a\nformula of Ni and Wu. As a consequence, for such links with unknotted\ncomponents, we characterize L-space surgery slopes in terms of the\n\ν+-invariants of the knots obtained from blowing down the components.\n We give a proof of a skein inequality for the d-invariants of +1\nsurgeries along linking number zero links that differ by a crossing change. We\nalso describe bounds on the smooth four-genus of links in terms of the\nh-function, expanding on previous work of the second author, and use these\nbounds to calculate the four-genus in several examples of links.\n