arXiv subjects

Alexander Barchechat

Publications and source records attributed to Alexander Barchechat.

2 recordsLinked to original sources

arXiv2004

Connected Sums of Closed Orientable Triangulated 3-Manifolds

In this paper, we describe geometrical constructions to obtain triangulations of connected sums of closed orientable triangulated 3-manifolds. Using these constructions, we show that it takes time polynomial in the number of tetrahedra to check if a closed orientable 3-manifold, equipped with a minimal triangulation, is reducible or not. This result can easily be generalized to compact orientable 3-manifolds with non-empty boundary.

math.GT↗

arXiv2003

Minimal Triangulations of Reducible 3-Manifolds

In this thesis, we use normal surface theory to understand certain properties of minimal triangulations of compact orientable 3-manifolds. We describe the collapsing process of normal 2-spheres and disks. Using some geometrical constructions to take connected sums of triangulated 3-manifolds, we obtain the following result: given a minimal triangulation of a closed orientable 3-manifold M, it takes polynomial time in the number of tetrahedra to check if M is reducible or not.

math.GT↗