Connected Sums of Closed Orientable Triangulated 3-Manifolds

Details Connected Sums of Closed Orientable Triangulated 3-Manifolds Connected Sums of Closed Orientable Triangulated 3-Manifolds

2004-04-19

arxiv.org/abs/math/0404309v1

Mathematics

Geometric Topology

Scientific paper

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.

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