Deciding nonconstructibility of 3-balls with strict spanning edges

TL;DR

This paper investigates the conditions under which a simplicial 3-ball with spanning edges cannot be constructed, providing a new criterion to decide nonconstructibility efficiently.

Contribution

It introduces a sufficient condition for nonconstructibility of simplicial 3-balls with spanning edges, advancing understanding of their combinatorial properties.

Findings

A new sufficient condition for nonconstructibility

Efficient decision method for certain 3-balls

Insights into the structure of simplicial 3-balls with spanning edges

Abstract

In this paper, we consider constructibility of simplicial 3-balls. In many cases, examining 1-dimensional subcomplexes of a simplicial 3-ball is efficient to solve the decision problem whether the simplicial 3-ball is constructible or not. From the point of view, we consider the case where a simplicial 3-ball has spanning edges and present a sufficient condition for nonconstructibility.