Embedding simply connected 2-complexes in 3-space -- II. Rotation systems

Abstract

We prove that 2-dimensional simplicial complexes whose first homology group is trivial have topological embeddings in 3-space if and only if there are embeddings of their link graphs in the plane that are compatible at the edges and they are simply connected.

References in corpus (3)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation
• Embedding simply connected 2-complexes in 3-space -- IV. Dual matroids

Cited by in corpus (3)

• Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation
• Embedding simply connected 2-complexes in 3-space -- IV. Dual matroids
• Multibranched surfaces in 3-manifolds