On Blocking Numbers of Surfaces

TL;DR

This paper proves that 2-dimensional manifolds with non-trivial fundamental groups have infinite blocking numbers unless they are flat, confirming a conjecture linking finiteness of blocking number to flatness.

Contribution

It establishes that non-flat 2D manifolds with non-trivial fundamental groups cannot have finite blocking numbers, advancing understanding of geometric blocking properties.

Findings

Non-flat 2D manifolds with non-trivial fundamental groups have infinite blocking numbers.

Finiteness of blocking number implies the manifold must be flat in this setting.

Abstract

The blocking number of a manifold is the minimal number of points needed to block out lights between any two given points in the manifold. It has been conjectured that if the blocking number of a manifold is finite, then the manifold must be flat. In this paper we prove that this is true for 2-dimensional manifolds with non-trivial fundamental groups.