Murasugi sum and extremal knot Floer homology
Zhechi Cheng
Wuhan University, Wuhan, ChinaMatthew Hedden
Michigan State University, East Lansing, USASucharit Sarkar
University of California, Los Angeles, USA
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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