Volume 22, issue 2 (2022)

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Heegaard Floer homology of surgeries on two-bridge links

Yajing Liu

Algebraic & Geometric Topology 22 (2022) 473–557

Heegaard Floer homology is combinatorially computable, but it is still unknown for many 3–manifolds, especially for HF of hyperbolic manifolds. We conduct some computations by utilizing the link surgery formula of Manolescu and Ozsváth. Using nice diagrams and algebraic methods, we show that HF and d–invariants of surgeries on a 2–bridge link L are determined only by the homotopy type of the As1,s2(L), where the maps in surgery complex by counting triangles are algebraically determined. Thus, this leads to a practical polynomial time algorithm. Using this algorithm, we calculate some examples explicitly: HF and the d–invariants of all integer surgeries on a family of hyperbolic two-bridge links including the Whitehead link.

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Heegaard Floer homology, link surgery, 2-bridge link
Mathematical Subject Classification 2010
Primary: 57M27, 57R58
Received: 26 February 2014
Revised: 8 July 2014
Accepted: 19 July 2020
Published: 3 August 2022
Yajing Liu
Department of Mathematics
Los Angeles, CA
United States