Pair-of-pants decompositions of 4-manifolds diffeomorphic to general type hypersurfaces

TL;DR

This paper demonstrates that certain complex hypersurfaces in projective 3-space can be decomposed into basic building blocks called 4-dimensional pair-of-pants, revealing new structural insights into their topology.

Contribution

It introduces a novel decomposition method for 4-manifolds diffeomorphic to high-degree hypersurfaces in complex projective space, combining pair-of-pants and K3 surface subsets.

Findings

Decomposition of hypersurfaces into pair-of-pants and K3 subsets

Explicit count of 4-dimensional pair-of-pants used in the decomposition

Structural understanding of complex hypersurfaces in 4-manifold topology

Abstract

In this paper, we show that a smooth 4-manifold diffeomorphic to a complex hypersurface in $\mathbb{CP}^3 $ of degree $d\geq 5$ can be decomposed as the union of $d(d-4)^2$ copies of 4-dimensional pair-of-pants and certain subsets of K3 surfaces.