Lower bound theorem for normal pseudomanifolds

TL;DR

This paper provides a combinatorial proof of the lower bound theorem for normal pseudomanifolds, explores equality cases, discusses related conjectures for spheres, and proposes a new conjecture for non-simply connected manifolds.

Contribution

It offers a self-contained combinatorial proof of the lower bound theorem and introduces a new conjecture for non-simply connected triangulated manifolds.

Findings

Proof of the lower bound theorem for normal pseudomanifolds

Analysis of equality cases in the theorem

Proposal of a new lower bound conjecture for non-simply connected manifolds

Abstract

In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower bound conjecture for triangulated spheres in the context of the lower bound theorem. Finally, we pose a new lower bound conjecture for non-simply connected triangulated manifolds.