An algorithmic strategy for finding characteristic maps over wedged simplicial complexes

Suyoung Choi and Mathieu Vallée

Vol. 320 (2022), No. 1, 13–43

DOI: 10.2140/pjm.2022.320.13

Abstract

The puzzle method was introduced by Choi and Park as an effective method for finding nonsingular 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.

Keywords

puzzle method, puzzle algorithm, algorithmic strategy, wedge operation, wedged simplicial complex, characteristic map, small covers, toric topology

Mathematical Subject Classification

Primary: 57-08, 57S12

Secondary: 05E45

Milestones

Received: 29 January 2022

Revised: 14 July 2022

Accepted: 24 July 2022

Published: 16 October 2022