Exterior Shifting of Low Genus Surfaces

TL;DR

This paper characterizes the exterior shiftings of triangulations of low genus surfaces such as the torus, projective plane, and Klein bottle, and provides an efficient algorithm for computing these shiftings.

Contribution

It offers a complete characterization of exterior shiftings for specific low genus surfaces and introduces a polynomial-time algorithm for their computation.

Findings

Characterization of exterior shiftings for low genus surfaces

Polynomial-time algorithm for computing exterior shiftings

Applicability to triangulations of the torus, projective plane, and Klein bottle

Abstract

We characterize the possible exterior shiftings of $K$, where $K$ runs over all triangulation of the torus, or the projective plane, or the Klein bottle. Further, we give a deterministic polynomial-time algorithm for computing the exterior shifting of a given triangulation $K$ as above.