Vol. 2, No. 2, 2017

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Longitudes in $\mathrm{SL}_2$ representations of link groups and Milnor–Witt $K_2$-groups of fields

Takefumi Nosaka

Vol. 2 (2017), No. 2, 211–233
Abstract

We describe an arithmetic K2-valued invariant for longitudes of a link L 3, obtained from an SL2 representation of the link group. Furthermore, we show a nontriviality on the elements, and compute the elements for some links. As an application, we develop a method for computing longitudes in SL˜2top() representations for link groups, where SL˜2top() is the universal covering group of  SL2().

Keywords
knot, Milnor $K$-group, Witt ring, parabolic representations, quandle
Mathematical Subject Classification 2010
Primary: 19C20, 19C30, 57M27, 57Q45
Secondary: 19C40, 57M10, 57M50
Milestones
Received: 30 June 2015
Revised: 4 March 2016
Accepted: 23 March 2016
Published: 14 December 2016
Authors
Takefumi Nosaka
Faculty of Mathematics
Kyushu University
744, Motooka
Nishi-ku, Fukuoka 819-0395
Japan