Baird's Conjecture

Baird's Conjecture is a hypothesis in topology, a field of mathematics studying shapes and spaces. It suggests that in certain highly symmetrical, smooth spaces (called manifolds), it's impossible to create a continuous, non-filtering map (called a graph homomorphism) from a structure resembling an infinite tree (like a branching network) into these spaces. Essentially, it predicts specific restrictions on how complex, highly connected nerve-like structures can be mapped into these spaces without losing key properties, highlighting deep relationships between the shape's global structure and the ways simpler networks can embed into them.