Four-genera of links and Heegaard Floer homology

Liu, Beibei

doi:10.2140/agt.2019.19.3511

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Four-genera of links and Heegaard Floer homology

Beibei Liu

Algebraic & Geometric Topology 19 (2019) 3511–3540

DOI: 10.2140/agt.2019.19.3511

Abstract

For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint oriented surfaces in $B^{4}$ . 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.

Keywords

four-genus bounds, $L$–space links, $d$–invariants

Mathematical Subject Classification 2010

Primary: 57M25, 57M27

References

Publication

Received: 1 June 2018

Revised: 4 February 2019

Accepted: 31 March 2019

Published: 17 December 2019

Authors

Beibei Liu
Department of Mathematics University of California, Davis Davis, CA United States

Volume 19, issue 7 (2019)