An algorithm to classify rational 3-tangles

Abstract

A $3$-$tangle$ $T$ is the disjoint union of $3$ properly embedded arcs in the unit 3-ball; it is called rational if there is a homeomorphism of pairs from $(B^3,T)$ to $(D^2\times I,\{x_1,x_2,x_3\}\times I)$. Two rational 3-tangles $T$ and $T^{\prime }$ are isotopic if there is an orientation-preserving self-homeomorphism $h:(B^3,T)\to (B^3,T^{\prime })$ that is the identity map on the boundary. In this paper, we give an algorithm to check whether or not two rational 3-tangles are isotopic by using a modified version of Dehn's method for classifying simple closed curves on surfaces.

Cited by in corpus (1)

• Uniqueness of reduced alternating rational 3-tangles