An algorithmic strategy for finding characteristic maps over wedged simplicial complexes

TL;DR

This paper enhances the puzzle method for identifying characteristic maps over wedged simplicial complexes, translating it into linear algebra and developing a constructive algorithm with performance analysis.

Contribution

It provides a linear algebraic formulation of the puzzle method and introduces a new constructive algorithm for finding characteristic maps.

Findings

The linear algebraic description simplifies the puzzle method.

The new algorithm is compared with existing methods, showing performance improvements.

The study advances computational techniques for topological analysis of simplicial complexes.

Abstract

The puzzle method was introduced by Choi and Park as an effective method for finding non-singular characteristic maps over wedged simplicial complexes $K(J)$ obtained from a given simplicial complex $K$. We study further the mod 2 case of the puzzle method. We firstly describe it completely in terms of linear algebraic language which allows us to develop a constructive puzzle algorithm. We also analyze our algorithm and compare its performances with other known algorithms including the Garrison and Scott algorithm.