Quandles over a hyperboloid of one sheet and the longitudinal mapping knot invariant for $SL(2,\mathbb{R})$

TL;DR

This paper explores algebraic structures called quandles on a hyperboloid of one sheet and computes the longitudinal mapping for the group $SL(2,\mathbb{R})$, contributing to knot invariants in geometric topology.

Contribution

It introduces a new class of quandles over a hyperboloid of one sheet and calculates the associated longitudinal mapping for $SL(2,\mathbb{R})$, advancing knot invariant theory.

Findings

Defined algebraic structures of quandles on a hyperboloid of one sheet.

Computed the longitudinal mapping for $SL(2,\mathbb{R})$.

Enhanced understanding of knot invariants related to these structures.

Abstract

This paper aims to consider algebraic structures of quandles defined over a hyperboloid of one sheet and compute the related longitudinal mapping for $SL(2,\mathbb{R})$.