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RASMUSSEN INVARIANTS OF SOME 4-STRAND PRETZEL KNOTS

  • KIM, SE-GOO ;
  • YEON, MI JEONG
  • Received : 2015.02.27
  • Accepted : 2015.04.03
  • Published : 2015.06.25

Abstract

It is known that there is an infinite family of general pretzel knots, each of which has Rasmussen s-invariant equal to the negative value of its signature invariant. For an instance, homologically ${\sigma}$-thin knots have this property. In contrast, we find an infinite family of 4-strand pretzel knots whose Rasmussen invariants are not equal to the negative values of signature invariants.

Keywords

Rasmussen invariant;knot signature;pretzel knot

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Acknowledgement

Supported by : National Research Foundation of Korea (NRF)