An algorithmic strategy for finding characteristic maps over wedged simplicial complexes (Q2090285)

The set of characteristic maps on a simplicial object \(K\) is a notion that was used by Davis-Januszkiewicz in the theory of small covers. The paper under review deals with the problem of finding all characteristic maps, mod2, on a simplicial complex \(K\). The starting point is a seed \(L\), a simplicial complex that cannot be obtained by applying a sequence of wedging operations from a given complex. Then, starting from \(CM(L)\), the authors describe a new puzzle algorithm for finding \(CM(L(J))\), with \(L(J)\) a PL-sphere, the characteristic maps after applying a sequence of \(J\) wedges on \(L\). The new algorithm provides a considerable improvement to the old algorithm that was presented in [\textit{S. Choi} and \textit{H. Park}, Isr. J. Math. 219, No. 1, 353--377 (2017; Zbl 1379.57043)]. The complexity of the algorithm depends on \(L\), the Picard number of \(L\), \(\mathrm{Pic}(L) = |V(L)| - \dim(L) + 1\), and the length of \(J\). The authors describe the algorithm and compute its complexity. Also, they describe the technical difficulties for extending the algorithm to integral characteristic maps.