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AAECC
2015
Springer

Computing fundamental groups from point clouds

8 years 7 months ago
Computing fundamental groups from point clouds
We describe an algorithm for computing a finite, and typically small, presentation of the fundamental group of a finite regular CW-space. The algorithm is based on the construction of a discrete vector field on the 3-skeleton of the space. A variant yields the homomorphism of fundamental groups induced by a cellular map of spaces. We illustrate how the algorithm can be used to infer information about the fundamental group π1(K) of a metric space K using only a finite point cloud X sampled from the space. In the special case where K is a d-dimensional compact manifold K ⊂ Rd , we consider the closure of the complement of K in the d-sphere MK = Sd \ K. For a base-point x in the boundary ∂MK of the manifold MK one can attempt to determine, from the point cloud X, the induced homomorphism of fundamental groups φ: π1(∂MK, x) → π1(MK, x) in the category of finitely presented groups. We illustrate a computer implementation for K a small closed tubular neighbourhood of a tame ...
Piotr Brendel, Pawel Dlotko, Graham Ellis, Mateusz
Added 27 Mar 2016
Updated 27 Mar 2016
Type Journal
Year 2015
Where AAECC
Authors Piotr Brendel, Pawel Dlotko, Graham Ellis, Mateusz Juda, Marian Mrozek
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