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Knot Invariants in Lens Spaces

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Knots, Low-Dimensional Topology and Applications (KNOTS16 2016)

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Abstract

In this survey we summarize results regarding the Kauffman bracket, HOMFLYPT, Kauffman 2-variable and Dubrovnik skein modules, and the Alexander polynomial of links in lens spaces, which we represent by mixed link diagrams. These invariants generalize the corresponding knot polynomials in the classical case. We compare the invariants by means of the ability to distinguish between some difficult cases of knots with certain symmetries.

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Acknowledgements

The first author was supported by the Slovenian Research Agency grants J1-8131, J1-7025, and N1-0064. The second author was supported by the Slovenian Research Agency grant N1-0083.

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering and Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Boštjan Gabrovšek

  2. Faculty of Education, University of Ljubljana, Kardeljeva ploščad 16, 1000, Ljubljana, Slovenia

    Eva Horvat

Authors
  1. Boštjan Gabrovšek
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  2. Eva Horvat
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Corresponding author

Correspondence to Boštjan Gabrovšek .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Williams College, Williamstown, MA, USA

    Colin C. Adams

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, USA

    Cameron McA. Gordon

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, USA

    Vaughan F.R. Jones

  4. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, USA

    Louis H. Kauffman

  5. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece

    Sofia Lambropoulou

  6. Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, USA

    Kenneth C. Millett

  7. Department of Mathematics, Columbian College of Arts & Sciences, George Washington University, Washington, DC, USA

    Jozef H. Przytycki

  8. Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy

    Renzo Ricca

  9. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Radmila Sazdanovic

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Gabrovšek, B., Horvat, E. (2019). Knot Invariants in Lens Spaces. In: Adams, C., et al. Knots, Low-Dimensional Topology and Applications. KNOTS16 2016. Springer Proceedings in Mathematics & Statistics, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-16031-9_17

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