In this paper we study some aspects of knots and links in lens spaces. Namely, if we consider lens spaces as quotient of the unit ball B3 with suitable identification of boundary points, then we can project the links on the equatorial disk of B3, obtaining a regular diagram for them. In this context, we obtain a complete finite set of Reidemeister type moves establishing equivalence, up to ambient isotopy, a Wirtinger type presentation for the fundamental group of the complement of the link and a diagrammatic method giving the first homology group. We also compute Alexander polynomial and twisted Alexander polynomials of this class of links, showing their correlation with Reidemeister torsion.
A. Cattabriga, E. Manfredi, M. Mulazzani (2013). On knots and links in lens spaces. TOPOLOGY AND ITS APPLICATIONS, 160(2), 430-442 [10.1016/j.topol.2012.12.001].
On knots and links in lens spaces
CATTABRIGA, ALESSIA;MANFREDI, ENRICO;MULAZZANI, MICHELE
2013
Abstract
In this paper we study some aspects of knots and links in lens spaces. Namely, if we consider lens spaces as quotient of the unit ball B3 with suitable identification of boundary points, then we can project the links on the equatorial disk of B3, obtaining a regular diagram for them. In this context, we obtain a complete finite set of Reidemeister type moves establishing equivalence, up to ambient isotopy, a Wirtinger type presentation for the fundamental group of the complement of the link and a diagrammatic method giving the first homology group. We also compute Alexander polynomial and twisted Alexander polynomials of this class of links, showing their correlation with Reidemeister torsion.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
