Spheres are rare

Abstract

We prove that triangulations of homology spheres in any dimension grow much slower than general triangulations. Our bound states in particular that the number of triangulations of homology spheres in 3 dimensions grows at most like the power 1/3 of the number of general triangulations.

14 pages, 1 figure

References in corpus (5)

• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Melons are branched polymers
• Scaling behaviour of three-dimensional group field theory
• Lost in Translation: Topological Singularities in Group Field Theory
• Trees of nuclei and bounds on the number of triangulations of the 3-ball

Cited by in corpus (6)

• Double Scaling in Tensor Models with a Quartic Interaction
• The Tensor Track, III
• Phase Transition in Tensor Models
• Maximizing the number of edges in three-dimensional colored triangulations whose building blocks are balls
• On the number of coloured triangulations of $d$-manifolds
• GEMs and amplitude bounds in the colored Boulatov model