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0111 · Nov 201719922001200920172026
4 results for pentachora

Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to algorithmically construct a trisection, which describes a 44-dimensional manifold as a uni…

2017-11-07abs ↗pdf ↗

We find vertex bounds for triangulated manifolds and apply them to 4-manifold complexity.

problem Finding vertex bounds for triangulated manifolds in arbitrary dimensions.
method Analyzing face numbers and proving bounds for triangulations of manifolds.
result We prove tight bounds for odd-dimensional manifolds and conjecture for even dimensions, with applications to 4-manifold complexity.