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Bordered Floer homology and a meridional class of knot

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

For a knot K and its knot Floer complex \(CFK^-(K)\), we introduce an algorithm to compute the bordered Floer bimodule of the complement of the knot and its meridian. The grading of the module computes \(spin^c\)-summands of \({\widehat{HFK}}(S^3_{-n}(K), \mu _K)\), which can also be extended to arbitrary framing n.

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Acknowledgements

The author would like to thank Kyungbae Park for the helpful discussion. Also thanks to Robert Lipshitz for pointing out the relation between this work and Hanselman’s trimodule [1]. Byungdo Park greatly helped revising the earlier version of this paper. Lastly, I would like to thank my advisor, Olga Plamenevskaya.

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  1. Pohang University of Science and Technology, Pohang, Republic of Korea

    Jaepil Lee

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  1. Jaepil Lee
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Correspondence to Jaepil Lee.

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Lee, J. Bordered Floer homology and a meridional class of knot. RACSAM 115, 65 (2021). https://doi.org/10.1007/s13398-021-01004-8

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  • DOI: https://doi.org/10.1007/s13398-021-01004-8

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