Immersions of punctured 4-manifolds: with applications to Quantum Cellular Automata

TL;DR

This paper explores the existence of immersions between smooth 4-manifolds, motivated by quantum cellular automata applications, revealing a partial order structure on closed 4-manifolds.

Contribution

It introduces a new perspective on 4-manifold immersions and their relation to quantum cellular automata, establishing a partial order among closed 4-manifolds.

Findings

Immersions induce a partial order on closed 4-manifolds

Applications to quantum cellular automata via pullback techniques

New insights into the topology of 4-manifolds

Abstract

Motivated by applications to pulling back quantum cellular automata from one manifold to another, we study the existence of immersions between certain smooth 4-manifolds. We show that they lead to a very interesting partial order on closed 4-manifolds.