Volume 19, issue 7 (2019)

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Four-genera of links and Heegaard Floer homology

Beibei Liu

Algebraic & Geometric Topology 19 (2019) 3511–3540

For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint oriented surfaces in B4. We use the h–function which is a link invariant from the Heegaard Floer homology to give lower bounds for the 4–genus of the link. For L–space links, the h–function is explicitly determined by the Alexander polynomials of the link and its sublinks. We show some L–space links where the lower bounds are sharp, and also describe all possible genera of disjoint oriented surfaces bounded by such links.

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four-genus bounds, $L$–space links, $d$–invariants
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Received: 1 June 2018
Revised: 4 February 2019
Accepted: 31 March 2019
Published: 17 December 2019
Beibei Liu
Department of Mathematics
University of California, Davis
Davis, CA
United States