Some problems of Applied & Computational Topology

05.03.2023 - 11.03.2023 | Będlewo


The main scope of the research group is: topological methods in estimating the minimal number of vertices which are necessary to triangulate a manifold or an action of finite group $G$ on a manifold. Another goal is the topological complexity and its computation and relation to the problem of minimal triangulation. We assume to complete two already started works in the form of publications and begin new join projects.
Particular subjects:
1. Estimates of equivariant covering type and minimal number of vertices of triangulation triangulating an action of finite group $G$ on a manifold (project in progress – advanced).
2. Improvement of the lower estimate of vertices that are necessary to triangulate the Poincare sphere from 12 to 13. It would be a step towards proving the Bjorner-Lutz conjecture that this number is equal to 16 (project in progress (partially advanced, a simplification of algorithm or more powerful computers are computers are required).
3. Modification of the BISTELLAR computer GAP software for minimizing given triangulation of a complex $K$ to adapt it to minimize $G$-invariant regular triangulation of an action of $G$ on $K$ (not began yet).

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