The upper bound theorem for flag homology 5-manifolds

TL;DR

This paper establishes an upper bound theorem for face numbers of flag homology 5-manifolds, identifying the join of three equal-length circles as the maximizer, and extends these bounds to certain pseudomanifolds.

Contribution

It proves a sharp upper bound theorem for face numbers of flag homology 5-manifolds and related pseudomanifolds, characterizing the extremal case explicitly.

Findings

Join of three equal-length circles maximizes face numbers

Upper bounds hold for flag Eulerian normal pseudomanifolds

Unique maximizer identified among all such manifolds

Abstract

We prove that among all flag homology $5$-manifolds with $n$ vertices, the join of $3$ circles of as equal length as possible is the unique maximizer of all the face numbers. The same upper bounds on the face numbers hold for $5$-dimensional flag Eulerian normal pseudomanifolds.