Complexity of 4-Manifolds

Abstract

We define and study a notion of complexity for smooth, closed and orientable 4-manifolds. This notion, based on the theory of Turaev shadows, represents the 4-dimensional analogue of Matveev's complexity of 3-manifolds. We classify complexity-0 and complexity-1 4-manifolds and provide examples of manifolds of higher complexity.

Keywords:

• 57N13
• 4-manifolds
• complexity
• polyhedra