Murasugi sum and extremal knot Floer homology

  • Zhechi Cheng

    Wuhan University, Wuhan, China
  • Matthew Hedden

    Michigan State University, East Lansing, USA
  • Sucharit Sarkar

    University of California, Los Angeles, USA
Murasugi sum and extremal knot Floer homology cover

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Abstract

The aim of this paper is to study the behavior of knot Floer homology under Murasugi sum. We establish a graded version of Ni’s isomorphism between the extremal knot Floer homology of Murasugi sum of two links and the tensor product of the extremal knot Floer homology groups of the two summands. We further prove that for each summand if and only if holds for the Murasugi sum (with and defined appropriately for multi-component links). Some applications are presented.

Cite this article

Zhechi Cheng, Matthew Hedden, Sucharit Sarkar, Murasugi sum and extremal knot Floer homology. Quantum Topol. (2024), published online first

DOI 10.4171/QT/186