Knot reversal acts non-trivially on the concordance group of topologically slice knots

• Taehee Kim ^[1] ; Charles Livingston ^[2]
  1. [1] Konkuk University

     Konkuk University

     Corea del Sur

     
  2. [2] Indiana University, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
• DOI: 10.1007/s00029-021-00751-1
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• Resumen

  • We construct an infinite family of topologically slice knots that are not smoothly concordant to their reverses. More precisely, if T denotes the concordance group of topologically slice knots and ρ is the involution of T induced by string reversal, then T/Fix(ρ) contains an infinitely generated free subgroup. The result remains true modulo the subgroup of T generated by knots with trivial Alexander polynomial.